Find the derivative of $f ( x ) = 2 x \left( 4 x ^ { 2 } + 1 \right) ^ { 7 }$
A) $\left( 112 x ^ { 2 } + 2 \right) \left( 4 x ^ { 2 } + 1 \right) ^ { 6 }$
B) $\left( 120 x ^ { 2 } + 2 \right) \left( 4 x ^ { 2 } + 1 \right) ^ { 7 }$
C) $\left( 120 x ^ { 2 } + 2 \right) \left( 4 x ^ { 2 } + 1 \right) ^ { 6 }$
D) $112 x ^ { 2 } \left( 4 x ^ { 2 } + 1 \right) ^ { 6 }$

Question

Quizplus · Accepted Answer

To find the derivative of $f(x) = 2x(4x^2 + 1)^7$, we use the product rule and the chain rule. The derivative is $f'(x) = 2(4x^2 + 1)^7 + 2x \cdot 7(4x^2 + 1)^6 \cdot 8x = (2 + 112x^2)(4x^2 + 1)^6 = (120x^2 + 2)(4x^2 + 1)^6$.

Find the Derivative Of f(x)=2x(4x2+1)7f ( x ) = 2 x \left( 4 x ^ { 2 } + 1 \right) ^ { 7 }f(x)=2x(4x2+1)7

Find the Derivative Of $f ( x ) = 2 x \left( 4 x ^ { 2 } + 1 \right) ^ { 7 }$