Question

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

Answer 1

`g'(x) = (5 *(25x^2-1))/((25x^2+1))- (4 * (16x^2-1))/((16x^2+1))`

Explanation:

Given that:

`g(x) = \int^(5x)_(4x) (u^2-1)/(u^2+1) \ \ du`

Then: the derivative of the function is as follows:

`g'(x) = ((5x)^2-1)/((5x)^2+1) \ \ (d)/(dx)(5x) -((4x)^2-1)/((4x)^2+1) \ \ (d)/(dx)(4x)`

`g'(x) = (5 *(25x^2-1))/((25x^2+1))- (4 * (16x^2-1))/((16x^2+1))`