Find the derivative.
-$$y = \sqrt [ 9 ] { x ^ { 2 } } + x ^ { e }$$
A) $\frac { 2 } { 9 x ^ { 7 / 9 } } + e x ^ { e }$
B) $\frac { 2 x ^ { 7 / 9 } } { 9 } + e x ^ { e - 1 }$
C) $\frac { 2 } { 9 x ^ { 7 / 9 } } + e x ^ { e - 1 }$
D) $\frac { 2 x ^ { 7 / 9 } } { 9 } + e x ^ { e }$

Question

Quizplus · Accepted Answer

Using the power rule and chain rule, we get:
$$\frac{d}{dx}(x^{2/9})=\frac{2}{9}x^{-7/9}$$
$$\frac{d}{dx}(x^e)=ex^{e-1}$$
Thus, the derivative of $y$ is:
$$\frac{dy}{dx}=\frac{2}{9}x^{-7/9}+ex^{e-1}$$
Simplifying and putting it in the given choices, we see that choice C is the correct one.

Find the Derivative y=x29+xey = \sqrt [ 9 ] { x ^ { 2 } } + x ^ { e }y=9x2​+xe

Find the Derivative $y = \sqrt [ 9 ] { x ^ { 2 } } + x ^ { e }$