Question

If $y=lo{g}_{cosx}sinx$ , then $\frac{dy}{dx}$ is equal to

• A. $\frac{\left(cotxlogcosx+tanxlogsinx\right)}{{\left(logcosx\right)}^2}$
• B. $\frac{\left(tanxlogcosx+cotxlogsinx\right)}{{\left(logcosx\right)}^2}$
• C. $\frac{\left(cotxlogcosx+tanxlogsinx\right)}{{\left(logsinx\right)}^2}$
• D. None of the above

Answer 1

Answer: (A)

Given, $y={\log }_{\cos x}\sin x=\frac{\log \sin x}{\log \cos x}$
On differentiating w.r.t. x, we get
$\frac{dy}{dx}=\frac{\cot x\cdot \log \cos x+\tan x\cdot \log \sin x}{(\log \cos x{)}^2}$