Derivative

[VBoy336]

I'm having problem with a problem =) can someone help.

finding derivative:
f(x) = 1/2x^2 + 3x^3

i know there is a shortcut way to derivative, but i did the long way and got

9x^2 - x

is that correct? if not, can you tell me the step to solve it? thanks

[courtrigrad]

f(x) = \frac{1}{2x^{2}} + 3x^{3} .

Use the power rule.

\frac{d}{dx} (2x^{2})^{-1} = -1(2x^{2})^{-2}(4x) = -\frac{1}{x^{3}} .

\frac{d}{dx} (3x^{3}) = 9x^{2} .

\frac{dy}{dx} = -\frac{1}{x^{3}} + 9x^{2}