$\text { Use the rules of differentiation to find the derivative of the function } g ( x ) = x ^ { 6 } + 5 x ^ { 3 } \text {. }$
A) $g ^ {t } ( x ) = 6 x ^ { 5 } + 3 x ^ { 2 }$
B) $g ^ { t } ( x ) = x ^ { 5 } + 5 x ^ { 2 }$
C) $g ^ { t} ( x ) = 6 x ^ { 5 } + 15 x ^ { 2 }$
D) $g ^ { t } ( x ) = 6 x ^ { 7 } + 15 x ^ { 4 }$
E) $g ^ { t } ( x ) = x ^ { 7 } + 5 x ^ { 4 }$

Question

$\text { Use the rules of differentiation to find the derivative of the function } g ( x ) = x ^ { 6 } + 5 x ^ { 3 } \text {. }$ 
A) $g ^ {t } ( x ) = 6 x ^ { 5 } + 3 x ^ { 2 }$
B) $g ^ { t } ( x ) = x ^ { 5 } + 5 x ^ { 2 }$
C) $g ^ { t} ( x ) = 6 x ^ { 5 } + 15 x ^ { 2 }$
D) $g ^ { t } ( x ) = 6 x ^ { 7 } + 15 x ^ { 4 }$
E) $g ^ { t } ( x ) = x ^ { 7 } + 5 x ^ { 4 }$

Quizplus · Accepted Answer

We use the power rule of differentiation, which states that the derivative of x^n is nx^(n-1). 
Therefore, g'(x) = 6x^5 + 15x^2. The correct option is C.

Use the rules of differentiation to find the derivative of the function g(x)=x6+5x3. \text { Use the rules of differentiation to find the derivative of the function } g ( x ) = x ^ { 6 } + 5 x ^ { 3 } \text {. } Use the rules of differentiation to find the derivative of the function g(x)=x6+5x3.

$\text { Use the rules of differentiation to find the derivative of the function } g ( x ) = x ^ { 6 } + 5 x ^ { 3 } \text {. }$