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

[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.

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

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

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

 

[tacman]

Yes, your answer is correct. To find the derivative of f(x), you can use the power rule, which states that the derivative of x^n is nx^(n-1). Applying this rule, we get:

f'(x) = (1/2)(2)x^(2-1) + (3)(3)x^(3-1)
= x + 9x^2

This is the same as your answer of 9x^2 - x. Great job!