Find the derivative of \(y = \sin^{2} (5x)\) with respect to x.
-
10 sin 5x cos 5x
- 5 sin5x cos 5x
- 2 sin 5x cos 5x
- 15 sin 5x cos 5x
The correct answer is: A
Explanation
\(y = \sin^{2} (5x)\)
Let u = sin 5x
\(\frac{\mathrm d u}{\mathrm d x} = 5 \cos 5x\)
\(\therefore y = u^{2}\)
\(\frac{\mathrm d y}{\mathrm d u} = 2u\)
\(\frac{\mathrm d y}{\mathrm d x} = 2u . 5 \cos 5x\)
= \(10u \cos 5x\)
= \(10 \sin 5x \cos 5x\)