Question

If $y=a^{\frac{1}{2}}{\log }_a\cos x$, find $\frac{dy}{dx}$.

Answer 1

We have,

$y=a^{1/2}{\log }_a\cos x$

On differentiating both sides w.r.t $x$, we get

$\frac{dy}{dx}=a^{1/2}\frac{1}{\cos x{\log }_{e}a}\times -\sin x$

$\frac{dy}{dx}=-a^{1/2}\frac{\tan x}{{\log }_{e}a}$

Hence, this is the answer.