Using the FTOC to find the derivative of the integral <msubsup> &#x222B;<!-- ∫ -->

gledanju0

gledanju0

Answered question

2022-06-06

Using the FTOC to find the derivative of the integral
x 2 5 ( 4 x + 2 ) d x .

Answer & Explanation

Patricia Curry

Patricia Curry

Beginner2022-06-07Added 15 answers

You have
f ( x ) = x 2 5 4 t + 2 d t
and you want to find f ( x ).
First note that
f ( x ) = 5 g ( x ) 4 t + 2 d t
where g ( x ) = x 2 . So f ( x ) is the composition of two functions:
f ( x ) = h ( g ( x ) ) .
where
h ( x ) = 5 x 4 x + 2 d t and g ( x ) = x 2 .
So by the chain rule you have
f ( x ) = h ( g ( x ) ) g ( x ) = ( 4 g ( x ) + 2 ) 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?