# Thread: What rule of differentiation to use?

1. ## What rule of differentiation to use?

I have the following problem;

Differentiate with respect to x;

y = (2x^5) - (3x^(1/4)) - (4/(x^7))

Now, I get that 2x^5 becomes 10x^4, and that 3x^(1/4) becomes 3/(4x^(3/4)), but what about the last part of the problem: 4/(x^7)?

Also, once I have figured that out, how do I get the final answer? Am I going in the right direction with this?

Pointing me in the direction of the techniques needed to answer the question would be appreciated more than just a direct answer.

Many thanks

2. ## Re: What rule of differentiation to use?

Remember that $\displaystyle \displaystyle \frac{4}{x^7} = 4x^{-7}$. Do you know what to do now?

3. ## Re: What rule of differentiation to use?

Ahhh! Cheers Prove it. I had an inkling that it had something to do with that. I was aware that x^(-y) was equivalent to 1/(x^y), but somehow it didn't click that this could be done with numbers on top larger than 1. Silly of me really.

So, taking that into account, the answer to the whole problem would be:

(10x^4) - (3x^(1/4)) - (-28x^(-8))

Is this correct? Or is there another step when the problem is in the form y = (function) - (function) - (function)?

4. ## Re: What rule of differentiation to use?

Originally Posted by Consumariat
Ahhh! Cheers Prove it. I had an inkling that it had something to do with that. I was aware that x^(-y) was equivalent to 1/(x^y), but somehow it didn't click that this could be done with numbers on top larger than 1. Silly of me really.

So, taking that into account, the answer to the whole problem would be:

(10x^4) - (3x^(1/4)) - (-28x^(-8))

Is this correct? Or is there another step when the problem is in the form y = (function) - (function) - (function)?
You have forgotten to differentiate the middle term...

5. ## Re: What rule of differentiation to use?

Originally Posted by Prove It
You have forgotten to differentiate the middle term...
Oops! You're right.

(10x^4) - ( 3/(4x^(3/4)) ) - (-28x^(-8))

So other than that, this is correct?

6. ## Re: What rule of differentiation to use?

Originally Posted by Consumariat
Oops! You're right.

(10x^4) - ( 3/(4x^(3/4)) ) - (-28x^(-8))

So other than that, this is correct?
Yes, of course you can simplify this further to $\displaystyle \displaystyle 10x^4 - \frac{3}{4x^{\frac{3}{4}}} + \frac{28}{x^8}$.

7. ## Re: What rule of differentiation to use?

Originally Posted by Prove It
Yes, of course you can simplify this further to $\displaystyle \displaystyle 10x^4 - \frac{3}{4x^{\frac{3}{4}}} + \frac{28}{x^8}$.
Thanks for the help.