Find the second derivative of the function. $f(x)=x\left(2 x^{2}-1\right)^{6}$
A) $\left(26 x^{2}-1\right)\left(2 x^{2}-1\right)^{5}$
B) $6 x\left(2 x^{2}-1\right)^{5}$
C) $24 x\left(2 x^{2}-1\right)^{4}\left(26 x^{2}-3\right)$
D) $30 x\left(2 x^{2}-1\right)^{4}$

Question

Quizplus · Accepted Answer

To find the second derivative, we need to take the derivative of $\frac{d}{dx}(x(2x^2-1)^6)$. Using the product rule and the chain rule, we get:
\begin{align*}
f'(x) &= (2x^2-1)^6 + x(6(2x^2-1)^5(4x)) \
&= (2x^2-1)^5(13x) \
f''(x) &= 26x(2x^2-1)^4 + (2x^2-1)^5(13) \
&= 13(2x^2-1)^4(2x+1)(26x^2-3) \
&= 24x(2x^2-1)^4(26x^2-3)
\end{align*}
Thus, the answer is C.

Find the Second Derivative of the Function f(x)=x(2x2−1)6f(x)=x\left(2 x^{2}-1\right)^{6}f(x)=x(2x2−1)6 A) (26x2−1)(2x2−1)5\left(26 x^{2}-1\right)\left(2 x^{2}-1\right)^{5}(26x2−1)(2x2−1)5

Find the Second Derivative of the Function $f(x)=x\left(2 x^{2}-1\right)^{6}$ A) $\left(26 x^{2}-1\right)\left(2 x^{2}-1\right)^{5}$