Question

differentiate cosx/x+sinx with respect to x​

Answer 1

Question:-To diffrentiate

$\frac{cosx}{x + sinx}$

with respect to x

Solution:-Using quotient rule of differenitaiation we get

$\frac{dy}{dx} = \frac{ - sinx}{1 + cosx} \\ \frac{dy}{dx} = \frac{ - sinx(1 - cosx)}{(1 + cosx)(1 - cosx)} \\ \frac{dy}{dx} = \frac{ - sinx(1 - cosx)}{(1 - {cos}^{2}x)} \\ \frac{dy}{dx} = \frac{ - sinx + sinxcosx}{ {sin}^{2}x} \\ \frac{dy}{dx} = \frac{ - 1}{sinx} + cotx \\ this \: will \: be \: the \: required \: diffrentiation \\ (hope \: it \: helps)$