Question

Derivative of $y=(sinx{)}^2$ with respect to x will be equal to

• A. $2sinx$
• B. $(cosx{)}^2$
• C. $sin2x$
• D. $2cosx$

Answer 1

The correct option is C $sin2x$

$\frac{d}{dx}\left[f\right(g\left(x\right)\left)\right]=f^{\prime }\left(g\right(x\left)\right).g^{\prime }\left(x\right)$
Here, $f\left(x\right)=x^2,g\left(x\right)=sinx{f}^{\prime }\left(x\right)=2xand{g}^{\prime }\left(x\right)=cosx$

Using chain rule,
$\frac{d}{dx}\left(\right(sinx{)}^2)=2sinx.cosx=sin2x$