Question

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

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

Answer 1

Answer: (A)

Let $y=\sin x^3,\therefore \frac{dy}{dx}=\cos x^3.3x^2$
$z=\cos x^3\frac{dz}{dx}=-\sin x^3.3x^2$
$\therefore \frac{dy}{dz}=\frac{dy/dx}{dz/dx}=-\frac{\cos x^3}{\sin x^3}=-\cot x^3$