Respuesta :
Answer:
[tex]f^{\prime}(2)=\frac{1}{\sqrt[]{9}}=\frac{1}{3}[/tex]Step by step explanation:
To determine the derivate of the following function:
[tex]\begin{gathered} f(x)=\sqrt[]{2x+5} \\ f(x)=(2x+5)^{\frac{1}{2}} \end{gathered}[/tex]To calculate the derivate of the function, we can use the power rule.
Take the power, 1/2, bring it in front of the parenthesis, and then reduced the power by 1.
[tex]f^{\prime}(x)=\frac{1}{2}(2x+5)^{-\frac{1}{2}}[/tex]Then, you have to derivate the intern, which means the parenthesis:
[tex]f^{\prime}(x)=\frac{1}{2}(2x+5)^{-\frac{1}{2}}\cdot2[/tex]Now, evaluate the derivate in x=2, to find f'(2).
[tex]\begin{gathered} f^{\prime}(x)=\frac{1}{\sqrt[]{2x+5}} \\ f^{\prime}(2)=\frac{1}{\sqrt[]{2(2)+5}} \\ f^{\prime}(2)=\frac{1}{\sqrt[]{9}}=\frac{1}{3} \end{gathered}[/tex]