Derivative of the integral of composite functions? L = &#x222B;<!-- ∫ --> f ( g (

Ayanna Trujillo

Ayanna Trujillo

Answered question

2022-06-08

Derivative of the integral of composite functions?
L = f ( g ( x ) ) d x, what is d L d g ( x ) ?

Answer & Explanation

Aiden Norman

Aiden Norman

Beginner2022-06-09Added 16 answers

Explanation:
Assume that g(x) is an invertible function, so that the function x(g) is well-defined. Then can apply a change of variables to the integral:
L = f ( g ) d g g ( x ( g ) ) d L d g = f ( g ) g ( x ( g ) ) .
If you want this in terms of x, it would be f ( g ( x ) ) / g ( x ).

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?