Question

Differentiate of 5-4x/5+4x

Answer 1

Step-by-step explanation:

We have,

$y = \frac{5 - 4x}{5 + 4x}$

$\implies \: \frac{dy}{dx} = \frac{ (5 + 4x)\dfrac{d}{dx} (5 - 4x) - (5 - 4x) \dfrac{d}{dx}(5 + 4x) }{(5 + 4x)^{2} }$

$\implies \: \frac{dy}{dx} = \frac{ ( - 4)(5 + 4x)-(4) (5 - 4x) }{(5 + 4x)^{2} }$

$\implies \: \frac{dy}{dx} = \frac{ - 20 - 16x-20 + 16x }{(5 + 4x)^{2} }$

$\implies \: \frac{dy}{dx} = \frac{ -40 }{(5 + 4x)^{2} }$