Differentiating Powers

fulhamfanincork

Any please tell me the method to differentiate powers please?

The question is....

5(the power sign)x

What do you mean by the power sign?

Is the question asking you to differentiate [latex]\displaystyle\mbox{5^x}[/latex], or, more likely, [latex]\displaystyle\mbox{x^5}[/latex]?

Fremen

[latex] 5^x = \left(e^{\log(5)}\right)^x = e^{x \log (5)} [/latex]

Now differentiate it like [latex]e^{ax}[/latex]

fulhamfanincork

Whoops. I mean the square root sign.

So the question is 5(square root sign)x

Fremen

[latex] 5 \sqrt{x} = 5 x^{\frac{1}{2}} [/latex]

That last bit will be in your textbook

LeixlipRed

Hmmm, think he means the 5th root of x.

Fremen

[latex] ^5 \sqrt{x} = x^{\frac{1}{5}} [/latex]

That last bit will be in your textbook

fulhamfanincork

Fremen wrote: »

[latex] ^5 \sqrt{x} = x^{\frac{1}{5}} [/latex]

That last bit will be in your textbook

Cheers. But is that the answer then?

LeixlipRed

No. You need to do the rest yourself.

fulhamfanincork

LeixlipRed wrote: »

No. You need to do the rest yourself.

I've looked in the book and I can't find anything.

I give up.

LeixlipRed

Please read the charter and don't do the problem for him again thanks!

LeixlipRed

fulhamfanincork wrote: »

I've looked in the book and I can't find anything.

I give up.

Ok so someone has already rewritten the fifth root of x for you in a different for, now all you need to use is the Power Rule.

Fremen

Yep. What's the derivative of [latex]x^n[/latex]?. How can you relate that to the problem you're trying to solve?

fulhamfanincork

Cheers for the help lads but I messed up the test.

Fremen

Don't give up so easily next time, then. You need to go back and learn your laws of exponents and logarithms properly.
Don't start a set of exercises until you have read and understood the theory developed in the text beforehand.
Go through it very slowly, line by line. It's maths, it's not designed to be read the way you read a novel.

callaway92

multiply the power by the coefficient and then take 1 away from the power

eg
Q) 4x²

A) 8x^1 (to the power of one)