Question

\(\dfrac{d}{dx}(\tan x+\sin^{2}x)=\) ?

• A. \(\sec x+2\sin x\cos x\)
• B. \(\sec^{2}x+\cos^{2}x\)
• C. \(\sec^{2}x+2\sin x\cos x\)
• D. \(\sec^{2}x-2\sin x\cos x\)

Hint:

\((\sin^{2}x)'=2\sin x\cos x\) comes from \((u^{2})'=2u\,u'\) with \(u=\sin x\).

Answer 1

The Correct Option is C

\((\tan x)'=\sec^{2}x\). Using chain rule on \(\sin^{2}x\): derivative \(=2\sin x\cos x\). Add to get \(\sec^{2}x+2\sin x\cos x\).