Find the derivative of the function.
-$f(x)=(3 x-3)(\sqrt{x}+4)$
A) $f^{\prime}(x)=2 x^{1 / 2}-1.5 x^{-1 / 2}+12$
B) $f^{\prime}(x)=4.5 x^{1 / 2}-1.5 x^{-1 / 2}+12$
C) $f^{\prime}(x)=2 x^{1 / 2}-3 x-1 / 2+12$
D) $f^{\prime}(x)=4.5 x^{1 / 2}-3 x^{-1 / 2}+12$

Question

Quizplus · Accepted Answer

The derivative is found using the product rule: $f'(x) = (3x-3)'(\sqrt{x}+4) + (3x-3)(\sqrt{x}+4)'$. This simplifies to $3(\sqrt{x}+4) + (3x-3)(\frac{1}{2}x^{-1/2})$, which results in $4.5x^{1/2} - 1.5x^{-1/2} + 12$.

Find the Derivative of the Function f(x)=(3x−3)(x+4)f(x)=(3 x-3)(\sqrt{x}+4)f(x)=(3x−3)(x​+4) A) f′(x)=2x1/2−1.5x−1/2+12f^{\prime}(x)=2 x^{1 / 2}-1.5 x^{-1 / 2}+12f′(x)=2x1/2−1.5x−1/2+12

Find the Derivative of the Function $f(x)=(3 x-3)(\sqrt{x}+4)$ A) $f^{\prime}(x)=2 x^{1 / 2}-1.5 x^{-1 / 2}+12$