Question

Find the derivative of the function. g(x)=∫5x4xu2−1u2+1 du.

Answer 1

Answer:

$g'(x) = \dfrac{5 *(25x^2-1)}{(25x^2+1)}- \dfrac{4 * (16x^2-1)}{(16x^2+1)}$

Step-by-step explanation:

Given that:

$g(x) = \int^{5x}_{4x} \dfrac{u^2-1}{u^2+1} \ \ du$

Then: the derivative of the function is as follows:

$g'(x) = \dfrac{(5x)^2-1}{(5x)^2+1} \ \ \dfrac{d}{dx}(5x) -\dfrac{(4x)^2-1}{(4x)^2+1} \ \ \dfrac{d}{dx}(4x)$

$g'(x) = \dfrac{5 *(25x^2-1)}{(25x^2+1)}- \dfrac{4 * (16x^2-1)}{(16x^2+1)}$