Question

The derivative of ${\sin }^{3}x{\cos }^{3}x$ is

• A. $\frac{3}{5}{\sin }^{2}2xcos2x$
• B. $\frac{3}{4}{\sin }^{2}2xcos2x$
• C. $\frac{3}{4}\sin 2xco{s}^{2}2x$
• D. $\frac{3}{2}{\sin }^{2}2xcos2x$

Answer 1

The correct option is B $\frac{3}{4}{\sin }^{2}2xcos2x$

$\frac{\alpha }{dx}\left({\sin }^{3}x{\cos }^{3}x\right)$

$=\frac{1}{8}\frac{\alpha }{dx}{\left(\sin 2x\right)}^3$

$=\frac{1}{8}3{\sin }^{2}2x\cos 2x\times 2$

$=\frac{3}{4}{\sin }^{2}2x\cos 2x$