Find the derivative of the function. $$f ( x ) = x ^ { 8 } \sqrt { 5 - 3 x }$$
A)$f ^ { t} ( x ) = \frac { x ^ { 7 } ( 5 - 51 x ) } { 2 \sqrt { 5 - 3 x } }$
B)$f ^ { t } ( x ) = \frac { x ^ { 7 } ( 80 - 3 x ) } { 2 \sqrt { 5 - 3 x } }$
C)$f ^ { t } ( x ) = \frac { x ^ { 7 } ( 80 + 51 x ) } { 2 \sqrt { 5 - 3 x } }$
D)$f ^ { t } ( x ) = \frac { x ^ { 7 } ( 5 + 3 x ) } { 2 \sqrt { 5 - 3 x } }$
E)$f ^ { t } ( x ) = \frac { x ^ { 7 } ( 80 - 51 x ) } { 2 \sqrt { 5 - 3 x } }$

Question

Quizplus · Accepted Answer

To find the derivative, use the product rule and chain rule. Rewrite the function as $f(x) = x^8 (5 - 3x)^{1/2}$. The derivative is $f'(x) = x^8 \cdot \frac{1}{2}(5 - 3x)^{-1/2}(-3) + 8x^7(5 - 3x)^{1/2}$. Simplifying gives the correct choice.

Find the Derivative of the Function f(x)=x85−3xf ( x ) = x ^ { 8 } \sqrt { 5 - 3 x }f(x)=x85−3x​

Find the Derivative of the Function $f ( x ) = x ^ { 8 } \sqrt { 5 - 3 x }$