317/1000 | Nth Order Differential Coefficient of tan^(-1)x | De Moivre's Theorem & Partial Fractions
In this Video, we will learn:
00:00 Find the Nth Order Differential Coefficient of tan^(-1)x
00:10 Find the Nth Order Differential Coefficient of tan inverse x
00:20 Find the Nth Order Derivative of tan inverse x
00:46 How do we know that which formula is applicable for nth order differential coefficient ?
01:14 Differentiation of tan inverse x with respect to x
02:00 🔴POINT OF MISTAKE🔴
03:20 Step 2- Partial fraction method for non-repeated linear factors in denominator
04:55 Step 3
06:00 Formula of nth Derivative of 1/(ax+b)
07:30 HINT
07:40 Step 4
10:00 Statement of De Moivre 's Theorem
12:00 nth Order Differential Coefficient of tan^-1(x)
# Description
In this video, we'll find the Nth order differential coefficient of tan^(-1)x using De Moivre's Theorem and partial fractions. We'll start by differentiating tan inverse x and then apply partial fractions to simplify the expression. We'll also discuss how to choose the correct formula for the nth order differential coefficient and provide a step-by-step solution.
# Hashtags
#DeMoivresTheorem #PartialFractions #NthOrderDifferentialCoefficient #Calculus #Mathematics
# Keywords
De Moivre's Theorem, partial fractions, Nth order differential coefficient, calculus, mathematics, tan inverse x, differentiation, nth derivative.
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316/1000 | Nth Order Derivative of y=x^(n-1)logx at x=1/2 | Leibnitz's Theorem | Calculus
Timestamps:
00:00 - Nth order Derivative of y=x^(n-1)logx
00:10 - Nth order Differential coefficient of y=x^(n-1)logx
00:20 Nth order Differential coefficient of y=x^(n-1)logx at x=1/2
00:50 - Simplification of y=x^(n-1)logx
01:33 Differentiation of y=x^(n-1)logx
03:35- Formula and trick to learn Leibnitz's Theorem
03:44 - Eligibility criteria of Leibnitz's Theorem
05:50 - (N-1)th Order Differential coefficient of xy1
07:34 (n-1)th order Derivative of x^(n-1)
07:44 Nth ORDER DERIVATIVE of x^m
07:55 Nth ORDER DERIVATIVE of x^m when m is greater than n
08:23 Nth ORDER DERIVATIVE of x^m when m=n
_Description_
In this video, we'll find the Nth order derivative of the function y=x^(n-1)logx using Leibnitz's Theorem. We'll start by simplifying the function and then apply the theorem to find the Nth order derivative. We'll also discuss the eligibility criteria for Leibnitz's Theorem and provide formulas and tricks to learn it.
_Hashtags_
#Calculus #LeibnitzTheorem #NthOrderDerivative #Mathematics #Derivatives
_Keywords_
calculus, Leibnitz's Theorem, Nth order derivative, mathematics, derivatives, x^(n-1)logx, logarithmic functions.
315/1000 | Nth Order Derivative of y = log(x³) | Calculus | Mathematics
Timestamps:
00:00 If y=logx³ then Nth order derivative of y is ?
00:20 Common Mistake Reminder
01:25 First order Derivative of y=logx³
02:25 Formula of Nth order Derivative of 1/(ax+b)
03:40 (n-1)th order Derivative of y=3/x
04:00 If y=logx³ then result of Nth order Derivative
_Description_
In this video, we'll find the Nth order derivative of the function y = log(x³). We'll start by finding the first-order derivative and then use a formula to find the Nth order derivative. We'll also discuss a common mistake to avoid and provide a step-by-step solution.
_Hashtags_
#Calculus #Mathematics #Derivatives #NthOrderDerivative #LogarithmicFunctions
_Keywords_
calculus, mathematics, derivatives, Nth order derivative, logarithmic functions, log(x³), derivative formulas.
314/1000 | Multivariable Partial Differentiation | Prove sin2x(∂u/∂x)+sin2y(∂u/∂y)+sin2z(∂u/∂z)=2
Timestamps:
00:00 If u=log(tanx+tany+tanz), then prove sin2x(∂u/∂x)+sin2y(∂u/∂y)+sin2z(∂u/∂z)=2
00:40 Multivariable Partial Differentiation
01:05 Partial Differentiation with respect to x taking y and z as constants
03:25 Partial Differentiation with respect to y taking x and z as constants
04:20 Partial Differentiation with respect to z taking x and y as constants
_Description_
In this video, we'll use multivariable partial differentiation to prove the given equation. We'll start by finding the partial derivatives of u with respect to x, y, and z, treating the other variables as constants. Then, we'll substitute these derivatives into the given equation and simplify to prove the result.
_Hashtags_
#MultivariableCalculus #PartialDifferentiation #Mathematics #Calculus #Proof
_Keywords_
multivariable calculus, partial differentiation, mathematics, calculus, proof, partial derivatives, multivariable functions.
313/1000 | Euler's Theorem in u=tan^-1{(x³+y³)/(x-y)} on Homogeneous Functions
Timestamps:
00:00 If u=tan^-1{(x³+y³)/(x-y)} , apply Euler's Theorem to find the Following Values,
00:40 Eligibility Criteria for Euler's Theorem
01:04 How to know that a function is Homogeneous or not ?
01:16 What is a Homogeneous Function
02:22 Reducible Homogenous Function
02:32 How to Express Homogeneous Function
04:29 How to find Degree of Homogeneous Function
05:19 Statement of Euler's Theorem
07:30 x(∂u/∂x)+y(∂u/∂y)=sin2u
08:13 2nd-order Euler's Theorem
09:30 If z is a Homogeneous Function in the variables x and y of degree n and z=f(u) then,
11:00 x²(∂²u/∂x²)+y²(∂²u/∂y²)+2xy(∂²u/∂y∂y)=sin4u-sin2u
11:30 x²(∂²u/∂x²)+y²(∂²u/∂y²)+2xy(∂²u/∂y∂y)=2sinucos3u
_Description_
In this video, we'll apply Euler's Theorem to find the degree of homogeneity of the function u=tan^-1{(x³+y³)/(x-y)}. We'll start by discussing the eligibility criteria for Euler's Theorem, homogeneous functions, and how to express and identify them. We'll then state Euler's Theorem and apply it to find the degree of homogeneity. Additionally, we'll cover 2nd-order Euler's Theorem and its application.
Introduction to the problem,
Eligibility Criteria for Euler's Theorem,
Identifying Homogeneous Functions,
Definition of Homogeneous Function,
Reducible Homogenous Function,
Expressing Homogeneous Function,
Finding Degree of Homogeneous Function,
Statement of Euler's Theorem,
Application of Euler's Theorem,
2nd-order Euler's Theorem,
Extension of Euler's Theorem,
Application of 2nd-order Euler's Theorem,
Alternative Form of 2nd-order Euler's Theorem,
_Hashtags_
#EulersTheorem #HomogeneousFunctions #Mathematics #Calculus #MultivariableCalculus #DegreeOfHomogeneity
_Keywords_
Euler's Theorem, homogeneous functions, mathematics, calculus, multivariable calculus, degree of homogeneity, reducible homogeneous function, 2nd-order Euler's Theorem.
312/1000 | Euler's Theorem on Homogeneous Functions | Degree of Homogeneity | Mathematics
Timestamps:
00:00 If u=(x³+y³)/(x+y) , apply Euler's Theorem to find the Following Values,
00:44 Statement of Euler's Theorem on Homogeneous Function
01:45 What is a Homogeneous Function
02:00 Expressing Homogeneous Function
02:22 How to find Degree of Polynomial
02:32 How to find Degree of Multivariable
03:44 Degree and Homogenity of u=(x³+y³)/(x+y)
03:54 How to find that the Function is Homogeneous or not ?
05:54 Result from Euler's Theorem
_Description_
In this video, we'll apply Euler's Theorem to find the degree of homogeneity of the function u=(x³+y³)/(x+y). We'll start by stating Euler's Theorem and explaining what a homogeneous function is. We'll then discuss how to express homogeneous functions, find the degree of polynomials and multivariable functions, and determine if a function is homogeneous. Finally, we'll use Euler's Theorem to find the result.
_Hashtags_
#EulersTheorem #HomogeneousFunctions #Mathematics #Calculus #MultivariableCalculus #DegreeOfHomogeneity
_Keywords_
Euler's Theorem, homogeneous functions, mathematics, calculus, multivariable calculus, degree of homogeneity, polynomials, multivariable functions.
311/1000 | Degree of a Polynomial: Definition, Examples, and Types | Algebra
_Timestamps_
0:00 - Definition of Degree of Polynomial
0:54 - Example of Degree of Polynomial
1:35 - Degree of Polynomial with variables in Multiplication
2:00 - Degree of Polynomial with variables in Division
2:24 - Degree of Polynomial in Multivariable
4:26 - Degree of Constant
5:00 - Difference between Polynomial and Equation
5:10 - Degree of Linear Equations
5:32 - Degree of Quadratic Polynomial
5:48 - Degree of Cubic Polynomial
6:08 - Degree of Quartic Polynomial
_Description_
In this video, we'll explore the concept of the degree of a polynomial, including its definition, examples, and different types. We'll cover topics such as the degree of polynomials with variables in multiplication and division, multivariable polynomials, constant polynomials, and more. We'll also discuss the difference between polynomials and equations, and examine the degree of linear, quadratic, cubic, and quartic polynomials.
_Hashtags_
#PolynomialDegree #Algebra #Mathematics #Polynomials #Equations #LinearEquations #QuadraticEquations #CubicEquations #QuarticEquations
_Keywords_
polynomial degree, algebra, mathematics, polynomials, equations, linear equations, quadratic equations, cubic equations, quartic equations, multivariable polynomials, constant polynomials.
310/1000 | Prove: Partial Differential Equation of y = f(x+at) + g(x-at)
Timestamps:
00:00 If y = f(x+at) + g(x-at) then show that.....
01:00 Partial Differentiation of y with respect to x taking t as a constant
02:10 Partial Differentiation of y with respect to t taking x as a constant
03:20 Substitution
03:30 Hence PROVE
_Description_
In this video, we'll prove a partial differential equation involving the function y = f(x+at) + g(x-at). We'll find the partial derivatives of y with respect to x and t, and then use substitution to prove the given statement.
_Hashtags_
#PartialDifferentialEquations #Calculus #Mathematics #MultivariableCalculus #Proof
_Keywords_
partial differential equations, calculus, mathematics, multivariable calculus, proof, partial derivatives, substitution method.
309/1000 | Reduction Formula for Integration of e^axsin^n(bx) | Indefinite Integral Proof
In this Video, we will learn:
00:00 Deduction of Reduction Formula of Integration of e^axsin^n(bx) with respect to x [Indefinite Integral]
00:15 Reduction Formula of Integration of e^axsin^n(bx)
00:25 What is the need of Reduction Formula
01:00 Integration of e^axsin^n(bx) by the help of Integration by Parts
08:00 Result : Proof of Reduction Formula of Integration of e^axsin^n(bx) with respect to x [Indefinite Integral]
_Description_
In this video, we'll derive the reduction formula for the indefinite integral of e^axsin^n(bx) with respect to x. We'll understand the need for reduction formulas, integrate e^axsin^n(bx) using integration by parts, and prove the reduction formula. This video is perfect for students of calculus and mathematics.
_Hashtags_
#ReductionFormula #Integration #Calculus #Mathematics #ExponentialFunction #TrigonometricFunctions #IndefiniteIntegral
_Keywords_
reduction formula, integration, calculus, mathematics, exponential function, trigonometric functions, e^axsin^n(bx), indefinite integral, integration by parts, proof.
308/1000 | Reduction Formula for Integration of cot^n(x) | Indefinite Integral | Trigonometric SubstitutionIn this Video, we will learn:
00:00 Deduction of Reduction Formula of Integration of cot^n(x) with respect to x [Indefinite Integral]
00:15 Reduction Formula of Integration of cot^n(x)
00:25 What is the need of Reduction Formula
01:00 Integration of cot^nx by the help of trigonometric substitution
02:00 Result : Proof of Reduction Formula of Integration of cot^nx with respect to x [Indefinite Integral]
*Description*
Learn how to derive the reduction formula for the integration of cot^n(x) with respect to x. This video covers the step-by-step deduction of the reduction formula, its need, and proof using trigonometric substitution. Watch till the end to understand the concept thoroughly.
*Hashtags*
#ReductionFormula #Integration #Trigonometry #Calculus #Mathematics #IndefiniteIntegral #TrigonometricSubstitution #Cotangent #MathTutorials #LearnMath
*Most Searching Keywords*
"reduction formula integration"
"cot^n(x) integration"
"indefinite integral of cot^n(x)"
"trigonometric substitution"
"calculus tutorials"
"mathematics tutorials"
307/1000 | Reduction Formula for Integration of tan^n(x) | Indefinite Integral Proof
In this Video, we will learn:
00:00 Deduction of Reduction Formula of Integration of tan^n(x) with respect to x [Indefinite Integral]
00:15 Reduction Formula of Integration of tan^n(x)
00:25 What is the need of Reduction Formula
01:00 Integration of tan^nx by the help of trigonometric substitution
03:00 Result : Proof of Reduction Formula of Integration of tan^nx with respect to x [Indefinite Integral]
_Description_
In this video, we'll derive the reduction formula for the indefinite integral of tan^n(x) with respect to x. We'll understand the need for reduction formulas, integrate tan^nx using trigonometric substitution, and prove the reduction formula. This video is perfect for students of calculus and mathematics.
_Hashtags_
#ReductionFormula #Integration #Calculus #Mathematics #Trigonometry #TangentFunction #IndefiniteIntegral
_Keywords_
reduction formula, integration, calculus, mathematics, trigonometry, tangent function, tan^n(x), indefinite integral, trigonometric substitution, proof.
