Find the Correct Derivative of f(x)

[fghtffyrdmns]

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?

 

[Bohrok]

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

Use the power rule and subtract one from that exponent.

 

[fghtffyrdmns]

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

1/2 - 1 = -1/2

 

[tara123]

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

 

[Bohrok]

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

 

[fghtffyrdmns]

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

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

 

[fghtffyrdmns]

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

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

Like this?

 

[Bohrok]

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

 

[fghtffyrdmns]

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 :/

 

[Bohrok]

What does the book say?