\(y = \sin^{2} (5x)\)

Let u = sin 5x

\(\frac{\mathrm d u}{\mathrm d x} = 5 \cos 5x\)

\(\therefore y = u^{2}\)

\(\frac{\mathrm d y}{\mathrm d u} = 2u\)

\(\frac{\mathrm d y}{\mathrm d x} = 2u . 5 \cos 5x\)

= \(10u \cos 5x\)

= \(10 \sin 5x \cos 5x\)