JAMB 2002 · UME · Q49

Find the derivative of $y = \sin^2(5x)$ with respect to $x$ .

Worked solution (try it first)

Write $y = (\sin5x)^2$ .
Chain rule: bring down the 2 to get $2\sin5x$ , then multiply by the derivative of $\sin5x$ , which is $5\cos5x$ .
So $\frac{dy}{dx} = 2\sin5x \times 5\cos5x$
$= 10\sin5x\cos5x$ , option C.