Question

find dy/dx if y =5-x/5+x​

Answer 1

Solution

Given

$\tt \implies \: \: \dfrac{dy}{dx} = \dfrac{5 - x}{5 + x}$

Using u/v Method

$\tt \implies \: \dfrac{d \bigg( \dfrac{u}{v} \bigg)}{dx} = \dfrac{ v\dfrac{du}{dx} - u \dfrac{dv}{dx} }{ {v}^{2} }$

we get

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

$\tt \implies \: \dfrac{dy}{dx} = \dfrac{(5 + x) \times - 1 - (5 - x) \times 1}{(5 + x) ^{2} }$

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

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

$\tt \implies \: \dfrac{dy}{dx} = \dfrac{ - 10}{(5 + x)^{2} }$