Question

The derivative of $\sin \left(x^3\right)w.r.t.\cos \left(x^3\right)$ is

• A. $-\tan \left(x^3\right)$
• B. $\tan \left(x^3\right)$
• C. $-\cot \left(x^3\right)$
• D. $\cot \left(x^3\right)$

Answer 1

The correct option is C $-\cot \left(x^3\right)$

derivative of $\sin \left(x^3\right)$ and $\cos \left(x^3\right)$ is $\frac{d}{dx}\left(\sin \right(x^3\left)\right)=\cos \left(x^3\right)\times 3x^2\frac{d}{dx}\left(\cos \right(x^3\left)\right)=-\sin \left(x^3\right)\times 3x^2$

Derivative of $sin\left(x^3\right)$ w.r.t $cos\left(x^3\right)$ is $\frac{\left(\frac{d}{dx}sin\right(x^3\left)\right)}{\left(\frac{d}{dx}cos\right(x^3\left)\right)}=\frac{cos\left(x^3\right)\times 3x^2}{-\sin \left(x^3\right)\times 3x^2}=-\cot \left(x^3\right)$