Find the derivative of the function. $f ( x ) = ( 4 x + 9 ) ^ { 9 }$
A) $36 ( 4 x + 9 ) ^ { 8 }$
B) $9 ( 4 x + 9 ) ^ { 8 }$
C) $9 x ( 4 x + 9 ) ^ { 8 }$
D) $36 x ( 4 x + 9 ) ^ { 8 }$

Question

Quizplus · Accepted Answer

To find the derivative of $f(x) = (4x + 9)^9$, use the chain rule. The outer function is $u^9$ where $u = 4x + 9$, and its derivative is $9u^8$. The derivative of the inner function $u = 4x + 9$ is 4. Applying the chain rule, multiply these derivatives together: $9(4x + 9)^8 \cdot 4 = 36(4x + 9)^8$.

Find the Derivative of the Function f(x)=(4x+9)9f ( x ) = ( 4 x + 9 ) ^ { 9 }f(x)=(4x+9)9

Find the Derivative of the Function $f ( x ) = ( 4 x + 9 ) ^ { 9 }$