Question

differentiate the function y=2x/x+1

Answer 1

$The \: \: answer \: \: is \: \: given \: \: below :\\ \\ RULE: \\ \\ We \: \: know \: \: that,\\ \\ \frac{d}{dx} ( \frac{u}{v} ) \\ \\ = \frac{v \frac{du}{dx} - u \frac{dv}{dx} }{ {v}^{2} }, \\ where \: \: u \: \: and \: \: v \: \: are \: \: functions \\ of \: \: x.\\ \\ SOLUTION: \\ \\ Given,\\ \\ y = \frac{2x}{x + 1} \\ \\ Now, \: \: differentiating \: \: both \: \: \\ sides \: \: with \: \: respect \: \: to \: \: x,\\ we \: \: get: \\ \\ \frac{dy}{dx} = \frac{d}{dx} ( \frac{2x}{x + 1} ) \\ \\ = \frac{(x + 1) \frac{d}{dx}(2x) - 2x \frac{d}{dx} (x + 1)}{ {(x + 1)}^{2} } \\ \\ = \frac{(x + 1) (2)- 2x(1)}{ {(x + 1)}^{2} } \\ \\ = \frac{2x + 2 - 2x}{ {(x + 1)}^{2} } \\ \\ = \frac{2}{ {(x + 1)}^{2} } \: \: \: (Answer) \\ \\ Thank \: \: you \: \: for \: \: the \: \: question.$