use the formal definition to find the derivative of ( g(x)=sqrt{6 x} ) at ( x = 4 ).\nfind ( g^{prime}(x) )…

use the formal definition to find the derivative of ( g(x)=sqrt{6 x} ) at ( x = 4 ).\nfind ( g^{prime}(x) ) for the given function.\n( g^{prime}(x)=\frac{sqrt{6}}{2 sqrt{x}} )\nfind ( g^{prime}(4) ). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. ( g^{prime}(4)=quad ) (type an exact answer.)\nb. the derivative does not exist.

use the formal definition to find the derivative of ( g(x)=sqrt{6 x} ) at ( x = 4 ).\nfind ( g^{prime}(x) ) for the given function.\n( g^{prime}(x)=\frac{sqrt{6}}{2 sqrt{x}} )\nfind ( g^{prime}(4) ). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. ( g^{prime}(4)=quad ) (type an exact answer.)\nb. the derivative does not exist.

Answer

Explanation:

Step1: Substitute (x = 4) into (g'(x))

We have (g'(x)=\frac{\sqrt{6}}{2\sqrt{x}}). Substituting (x = 4) gives (g'(4)=\frac{\sqrt{6}}{2\sqrt{4}}).

Step2: Simplify the expression

Since (\sqrt{4}=2), then (g'(4)=\frac{\sqrt{6}}{2\times2}=\frac{\sqrt{6}}{4}).

Answer:

A. (g'(4)=\frac{\sqrt{6}}{4})