Question

find the derivative of ( f(x) ).

( f(x)=sin (x) )

( f^{prime}(x)= )

Explanation:

Step1: Recall derivative of sine

The derivative of \( \sin(x) \) with respect to \( x \) is a standard calculus result. The formula for the derivative of \( \sin(u) \) (where \( u = x \), so \( \frac{du}{dx}=1 \)) is \( \cos(u)\cdot\frac{du}{dx} \).

Step2: Apply the formula

For \( f(x)=\sin(x) \), using the derivative rule \( \frac{d}{dx}[\sin(x)] = \cos(x) \), we get \( f'(x)=\cos(x) \).

Answer:

\( \cos(x) \)