Question

Differentiate the following questions w.r.t. x.

$log\left(cos{e}^x\right).$

Answer 1

Ley y = $log\left(cos{e}^x\right).$

Dofferentiate both sides w.r.t. x, we get

$\frac{dy}{dx}=\frac{d}{dx}\left[log\right\{cos\left(e^x\right)\left\}\right]=\frac{1}{cos\left(e^x\right)}\frac{d}{dx}\left\{cos\right(e^x\left)\right\}\left(Usingchianrule\right)=\frac{1}{cos\left(e^x\right)}\{-sin(e^x\left)\right\}\frac{d}{dx}\left(e^x\right)\left(Usingchainrule\right)=-tan\left(e^x\right).e^x=-e^{x}tan\left(e^x\right)$