# Power rule

1. Sep 20, 2009

### fghtffyrdmns

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

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

3. The attempt at a solution

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

However, this is wrong. Why?

2. Sep 20, 2009

### Bohrok

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

Use the power rule and subtract one from that exponent.

3. Sep 20, 2009

### fghtffyrdmns

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

1/2 - 1 = -1/2

4. Sep 20, 2009

### tara123

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

5. Sep 20, 2009

### Bohrok

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

6. Sep 20, 2009

### fghtffyrdmns

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

7. Sep 20, 2009

### fghtffyrdmns

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

Like this?

8. Sep 20, 2009

### Bohrok

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

9. Sep 20, 2009

### fghtffyrdmns

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

10. Sep 21, 2009

### Bohrok

What does the book say?