Question

If $y=\tan \left(logx\right)$ then find $\frac{dy}{dx}$.

Answer 1

$y=\tan \left(\log x\right)$

Let $\log x=t$

Question becomes $\frac{dy}{dx}=\tan \left(t\right)$

Then $\frac{dy}{dx}$=${\sec }^{2}t$ $\times$$\frac{dt}{dx}$

Since $t=logx$

So $\frac{dt}{dx}$=$\frac{1}{x}$

Now $\frac{dy}{dx}$ =${\sec }^2\log x$$\times$ $\frac{1}{x}$