Question

The derivative of $\sin x^3$ $w.r.t.$ $\cos x^3$ is equal to

• A. $-\tan x^3$
• B. $-\cot x^3$
• C. $\cot x^3$
• D. $\tan x^3$

Answer 1

The correct option is B $-\cot x^3$

$\frac{d}{dx}\left(\sin x^3\right)=\cos x^3\times 3x^2$
$\frac{d}{dx}\left(\cos x^3\right)=-\sin x^3\times {3x}^2$
$\therefore \frac{d\left(\sin x^3\right)}{d\left(\cos x^3\right)}=-\cot x^3$