Question

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:

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