Question

If $y={\tan }^2\left(\log x^3\right)$, find $\frac{dy}{dx}$.

Answer 1

Given $y=ta{n}^2\left(log{x}^3\right)$

We need to find $\frac{dy}{dx}$

Consider $y=ta{n}^2\left(log{x}^3\right)$

$\Rightarrow y=ta{n}^2\left(3logx\right)$

$\Rightarrow y=\left[tan\right(3logx){]}^2$

Differentiate with respect to $x$ on both sides we get

$\Rightarrow \frac{dy}{dx}=2\left[tan\right(3logx\left)\right]\cdot se{c}^2\left(3logx\right)\cdot \frac{3}{x}$

$\Rightarrow \frac{dy}{dx}=\frac{6}{x}\cdot \left[tan\right(3logx\left)\right]\cdot se{c}^2\left(3logx\right)$

$\therefore \frac{dy}{dx}=\frac{6}{x}\cdot \left[tan\right(log{x}^3\left)\right]\cdot se{c}^2\left(log{x}^3\right)$