Question

If g is the inverse of function f and f'(x)=sin x, then g'(x) is equal to

• A. \(\cos\{g(x)\}\)
• B. \(\sin\{g(x)\}\)
• C. \(\dfrac{1}{\sin\{g(x)\}}\)
• D. None of these

Hint:

Derivative of inverse: (f⁻1)'(x)=1/f'(f⁻1(x)).

Answer 1

The Correct Option is C

For inverse functions, g'(x)=(1)/(f'(g(x))) ⟹ g'(x)=(1)/(sin(g(x)))