if ( g(x)=sin(x) ) then ( g^{prime}(x)= ) ( g^{prime}(5)= )

Explanation:

Step1: Find the derivative of (g(x)=\sin(x))

The derivative of (\sin(x)) with respect to (x) is (\cos(x)). So, (g^{\prime}(x)=\cos(x)).

Step2: Evaluate (g^{\prime}(x)) at (x = 5)

Substitute (x = 5) into (g^{\prime}(x)=\cos(x)). Then (g^{\prime}(5)=\cos(5)).

Answer:

(g^{\prime}(x)=\cos(x)) (g^{\prime}(5)=\cos(5))