Calculate the derivative of the function. Then find the value of the derivative as specified.
-$$g ( x ) = x ^ { 3 } + 5 x ; g ^ { \prime } ( 1 )$$
A) $g ^ { \prime } ( x ) = 3 x ^ { 2 } ; g ^ { \prime } ( 1 ) = 3$
B) $g ^ { \prime } ( x ) = 3 x ^ { 2 } + 5 x ; g ^ { \prime } ( 1 ) = 8$
C) $g ^ { \prime } ( x ) = 3 x ^ { 2 } + 5 ; g ^ { \prime } ( 1 ) = 8$
D) $g ^ { \prime } ( x ) = x ^ { 2 } + 5 ; g ^ { \prime } ( 1 ) = 6$

Question

Quizplus · Accepted Answer

To find the derivative of the function g(x), we take the derivative of each term separately. The derivative of x^3 is 3x^2, and the derivative of 5x is simply 5. Therefore, the derivative of g(x) is g'(x) = 3x^2 + 5. To find g'(1), we substitute x = 1 into the equation for the derivative to get g'(1) = 3(1)^2 + 5 = 8. Therefore, the correct choice is C, g'(x) = 3x^2 + 5; g'(1) = 8.

Calculate the Derivative of the Function g(x)=x3+5x;g′(1)g ( x ) = x ^ { 3 } + 5 x ; g ^ { \prime } ( 1 )g(x)=x3+5x;g′(1)

Calculate the Derivative of the Function $g ( x ) = x ^ { 3 } + 5 x ; g ^ { \prime } ( 1 )$