Question

Find the derivative of the function. g(x) = ∫5 x 4 x u2 − 1u2 +1 dug'(x) = g

Answer 1

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

Explanation:

The question can be better structured and represented as :

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

now the derivative of the function of g(x) is g'(x) which is equal to:

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

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