need help understanding d/dx(x^(1/2))

Hi,

I'm having problems understanding the derivation of fraction exponents like this for example:

d/dx(x^(1/2))

Obviously I have more complicated problems than this to evaluate, but a basic explanation would be helpful.

The book I'm using for some reason skips talking about this....

The example I'm looking at on my homework is this:

d/dx((4/z^(1/3))-(z^(1/4)))

4 over the 3rd root of z, minus z to the 4th root.

Thanks much,

sig

Re: need help understanding d/dx(x^(1/2))

Quote:

Originally Posted by

**sig** Hi,

I'm having problems understanding the derivation of fraction exponents like this for example:

d/dx(x^(1/2))

There is one basic power rule:

Thus

Re: need help understanding d/dx(x^(1/2))

Quote:

Originally Posted by

**Plato** There is one basic power rule:

Thus

I must be making mistakes when I evaluate then, because I know the power rule.

For instance my answer sheet says

I would think the x^(-1/2) would go on top of the fraction, and I don't know how the negative is pulled out of the exponent into the front of the answer. (Nerd)

Re: need help understanding d/dx(x^(1/2))

Quote:

Originally Posted by

**sig** my answer sheet says

I would think the x^(-1/2) would go on top of the fraction, and I don't know how the negative is pulled out of the exponent into the front of the answer. (Nerd)

Your answer sheet is wrong,

It should be

Recall that

Re: need help understanding d/dx(x^(1/2))

Quote:

Originally Posted by

**Plato** Your answer sheet is wrong,

It should be

Recall that

Oh I'm sorry, the negative was a part of a different problem.

Oh, and now I see how the numbers end up on bottom; the negative exponent.

OK thank you very much, I'll try some equations again and see if I can understand better.

-sig

Re: need help understanding d/dx(x^(1/2))

Hello, I'm back.

After looking and working on this equation,

I've come to the pre-simplified answer of:

-(4/3z^(4/3))-(1/(4z^(3/4))

And when I look the answer up on WRA, it gives the simplified answer of:

-((3z^(7/12)+16)/(12z^(4/3))

and I'm not seeing how this simplification is working.

Can anyone help explain?

Thanks..

-sig

Re: need help understanding d/dx(x^(1/2))

Quote:

Originally Posted by

**sig** Hello, I'm back.

After looking and working on this equation,

That is

Re: need help understanding d/dx(x^(1/2))

Quote:

Originally Posted by

**Plato** That is

Yes I got that much.

which equals

-(4/3z^(4/3))

But I don't see how this:

-(4/3z^(4/3)) - (1/4z^(/34))

turns into this:

- ((3z^(7/12)+16)/(12z^(4/3)))

Sorry for not entering this into special text- is there a way to convert without manually coding it?

Re: need help understanding d/dx(x^(1/2))

Re: need help understanding d/dx(x^(1/2))

Yes that's right and this above is where I can get to. But here below I don't understand

Re: need help understanding d/dx(x^(1/2))

nevermind figured it out, thanks!

~sig

Re: need help understanding d/dx(x^(1/2))

Re: need help understanding d/dx(x^(1/2))

Thanks Reck,

I had been thinking combining fractional exponents were like combining fractions but I was totally wrong!

More than helpful, I'll be back sometime soon, I know it.

~sig