Question

If f(x)=sinx, then f'(pi/3)=

Answer 1

- The function given is

`f(x)=\sin x`

- We are asked to find

`f^(\prime)((\pi)/(3))`

- The differentiation of the sine function gives:

`f^(\prime)(x)=(d)/(dx)(\sin x)=\cos x`

- Thus, we can solve the question by simply substituting π/3 into the function f'(x).

- That is,

`\begin{gathered} f^(\prime)(x)=\cos x \\ put\text{ }x=(\pi)/(3) \\ \\ \therefore f^(\prime)((\pi)/(3))=\cos(\pi)/(3)=(1)/(2) \end{gathered}`

Final Answer

The answer is

`f^(\prime)((\pi)/(3))=(1)/(2)`