$\text { Find the derivative of the algebraic function } f ( x ) = \left( x ^ { 6 } + 4 \right) ^ { 5 } \text {. }$
A) $f ^ {t} ( x ) = 5 x ^ { 5 } \left( x ^ { 6 } + 4 \right) ^ { 4 }$
B)$f ^ {t } ( x ) = 6 x ^ { 5 } \left( x ^ { 6 } + 4 \right) ^ { 4 }$
C) $f ^ { t} ( x ) = 30 x ^ { 5 } \left( x ^ { 6 } + 4 \right) ^ { 4 }$
D) $f ^ { t } ( x ) = 30 x ^ { 7 } \left( x ^ { 6 } + 4 \right) ^ { 4 }$
E) $f ^ { t } ( x ) = 30 x ^ { 6 } \left( x ^ { 6 } + 4 \right) ^ { 4 }$

Question

$\text { Find the derivative of the algebraic function } f ( x ) = \left( x ^ { 6 } + 4 \right) ^ { 5 } \text {. }$ 
A) $f ^ {t} ( x ) = 5 x ^ { 5 } \left( x ^ { 6 } + 4 \right) ^ { 4 }$
B)$f ^ {t } ( x ) = 6 x ^ { 5 } \left( x ^ { 6 } + 4 \right) ^ { 4 }$
C) $f ^ { t} ( x ) = 30 x ^ { 5 } \left( x ^ { 6 } + 4 \right) ^ { 4 }$
D) $f ^ { t } ( x ) = 30 x ^ { 7 } \left( x ^ { 6 } + 4 \right) ^ { 4 }$
E) $f ^ { t } ( x ) = 30 x ^ { 6 } \left( x ^ { 6 } + 4 \right) ^ { 4 }$

Quizplus · Accepted Answer

Using the chain rule, the derivative of $f(x) = (x^6 + 4)^5$ is $f'(x) = 5(x^6 + 4)^4 \cdot 6x^5$, which simplifies to $30x^5(x^6 + 4)^4$.

Find the derivative of the algebraic function f(x)=(x6+4)5. \text { Find the derivative of the algebraic function } f ( x ) = \left( x ^ { 6 } + 4 \right) ^ { 5 } \text {. } Find the derivative of the algebraic function f(x)=(x6+4)5.

$\text { Find the derivative of the algebraic function } f ( x ) = \left( x ^ { 6 } + 4 \right) ^ { 5 } \text {. }$