Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The question can be better structured and represented as :

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

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

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

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