Find the derivative.
-$y = x ^ { 3 / 4 }$
A) $\frac { 3 } { 4 } \mathrm { x } ^ { 1 / 4 }$
B) $\frac { 4 } { 3 } \times 1 / 3$
C) $\frac { 3 } { 4 } x ^ { - 1 / 4 }$
D) $\frac { 3 } { 4 } x ^ { - 3 / 4 }$

Question

Quizplus · Accepted Answer

We use the power rule of differentiation, which says that if

$$f(x)=x^n,$$

then

$$f'(x)=nx^{n-1}.$$

Thus, if

$$y=x^{3/4},$$

then

$$y'=\frac{3}{4}x^{-1/4}=\frac{3}{4}\frac{1}{\sqrt[4]{x}}=\frac{3}{4\sqrt[4]{x}}.$$

Therefore, the correct choice is $\boxed{	extbf{(C) } \frac{3}{4}x^{-1/4}}$.

Find the Derivative y=x3/4y = x ^ { 3 / 4 }y=x3/4

Find the Derivative $y = x ^ { 3 / 4 }$