Question

If $y={\sin }^2\theta +{\cos }^3\theta$. Find $\frac{dy}{d\theta }$.

• A. $2\cos \theta -3{\sin }^2\theta$
• B. $2\sin \theta {\cos }^2\theta -3{\cos }^2\theta$
• C. $2\sin \theta \cos \theta -3\sin \theta {\cos }^2\theta$
• D. $2\sin \theta \cos \theta -3{\sin }^2\theta \cos \theta$

Answer 1

The correct option is C $2\sin \theta \cos \theta -3\sin \theta {\cos }^2\theta$

Given, $y={\sin }^2\theta +{\cos }^3\theta$
So, $\frac{dy}{d\theta }=\frac{d({\sin }^2\theta +{\cos }^3\theta )}{d\theta }$
Using chain rule we have
$\frac{d{\sin }^2\theta }{d\sin \theta }\times \frac{d\sin \theta }{d\theta }+\frac{d{\cos }^3\theta }{d\cos \theta }\times \frac{d\cos \theta }{d\theta }$
$\Rightarrow 2\sin \theta \cos \theta -3\sin \theta {\cos }^2\theta$