Mastering Partial Differentiation: A Comprehensive Guide

Click For Summary
SUMMARY

The discussion centers on the confusion between integration by parts and partial differentiation. The correct formula for the derivative of a product of two functions is established as $\dfrac{d}{dx}[f(x)h(x)] = f’(x)h(x) + f(x)h’(x)$. The integration by parts formula is also referenced, highlighting the relationship between differentiation and integration. The participant clarifies that the problem at hand is related to integration by parts, not partial differentiation.

PREREQUISITES
  • Understanding of basic calculus concepts, including derivatives and integrals.
  • Familiarity with the product rule for differentiation.
  • Knowledge of the integration by parts technique.
  • Ability to manipulate and solve equations involving functions.
NEXT STEPS
  • Study the product rule in calculus to solidify understanding of derivatives.
  • Learn the integration by parts formula and its applications in solving integrals.
  • Practice problems involving both differentiation and integration to enhance problem-solving skills.
  • Explore advanced calculus topics such as multivariable calculus and partial derivatives for further learning.
USEFUL FOR

Students, educators, and anyone looking to deepen their understanding of calculus, particularly in differentiating and integrating functions.

jaychay
Messages
58
Reaction score
0
Untitled 4.png


Can you please help me ?
I have tried to do it many times but I end up getting the wrong answer.
Thank you in advance.
 
Physics news on Phys.org
I finally got the answer to the question.
Untitled 5.png
 
$\dfrac{d}{dx}[f(x)h(x)] = f’(x)h(x) + f(x)h’(x)$

$\displaystyle f(x)h(x) = \int f’(x)h(x) \, dx + \int f(x)h’(x) \, dx$

$\displaystyle (x+1)^5 = \sin{x} + \int f(x)h’(x) \, dx$

finish it ...
 
I think this is a problem on "integration by parts", NOT "partial differentiation".
 

Similar threads

Undergrad Integral confusion for a simple Differential Equation
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad How do I format equations correctly? (Curl, etc.)
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Vector calculus - Prove a function is not differentiable at (0,0)
  • · Replies 1 ·
Replies
1
Views
2K
High School Product rule OR Partial differentiation
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Lipschitz continuity of vector-valued function
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Partial differentiation of integral
  • · Replies 4 ·
Replies
4
Views
1K
Graduate How to solve this partial derivative which includes a summation?
  • · Replies 6 ·
Replies
6
Views
6K
Graduate Partial / Total Derivative, Compositions
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Confused About the Chain Rule for Partial Differentiation
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Understanding Mixed Partial Derivatives: How Do You Solve Them?
  • · Replies 3 ·
Replies
3
Views
2K