# Power rule

## Homework Statement

I promise this will be my last one :p

For this function: $$f(x)=-4x^{3}+\frac{3}{x}+\sqrt{x}-2$$
What would be the derivative using the power rule?

## Homework Equations

$$f(x)=-4x^{3}+\frac{3}{x}+\sqrt{x}-2$$

## The Attempt at a Solution

$$f'(x)=-12x^{2}-3x^{-2}-\frac{\sqrt{x}}{2}$$

However, this is wrong. Why?

$$\sqrt{x} = x^\frac{1}{2}$$

Use the power rule and subtract one from that exponent.

$$f'(x)=-12x^{2}-3x^{-2}+\frac{1}{2x^{1/2}}$$

1/2 - 1 = -1/2

derivative of x^1/2 = 1/2 x^(-1/2)

The exponent is -1/2, but that term should be positive.

derivative of x^1/2 = 1/2 x^(-1/2)

Could that be written as $$\frac{1}{2\sqrt{x}}$$?

The exponent is -1/2, but that term should be positive.

$$f'(x)=-12x^{2}-3x^{-2}+\frac{1}{2x^{1/2}}$$

Like this?

Yes, that's right. Didn't see your other post with the correct answer.

Yes, that's right. Didn't see your other post with the correct answer.

I edited it :D
I was just wondering because the book has a much different answer :/

What does the book say?