Question

If f(x) = log (sin x), find derivative of f(x)
1. tan x
2. sec x
3. cosec x
4. cot x

Answer 1

Correct Answer - Option 4 : cot x

Concept:

Chain rule: \(\rm \frac{d}{dx}[f(g(x))]= f'(g(x)) g'(x)\)

If y = log x, then f'(x) = 1/x

And if y = sin x, then f'(x) = cos x

Calculation:

f(x) = log (sin x)

Differentiating with respect to x, we get

⇒ f'(x) = (\(\rm \frac{1}{sin\ x}\))\(\rm \frac{d \sin \ x\ }{dx}\) 

⇒ f'(x) = \(\rm \frac{cos \ x}{sin \ x}\)

⇒ f'(x) = cot x