- Thread starter
- #1

#### coolbeans33

##### New member

- Sep 19, 2013

- 23

^{-3/5}

are there any derivative rules I can use for this problem?

- Thread starter coolbeans33
- Start date

- Thread starter
- #1

- Sep 19, 2013

- 23

are there any derivative rules I can use for this problem?

- Admin
- #2

- Mar 5, 2012

- 8,774

Welcome to MHB, coolbeans33!

Just the regular ones should do.^{-3/5}

are there any derivative rules I can use for this problem?

I presume you know that the derivative of $x^n$ is $nx^{n-1}$?

This is also true if n is a real number.

Or put otherwise: the derivative of $t^\alpha$ is $\alpha t^{\alpha - 1}$ for any real number $\alpha$.

- Thread starter
- #3

- Sep 19, 2013

- 23

so the answer is -3t

Last edited:

- Admin
- #4

Yes, although I would only use decimal notation if the exponent is given using such notation. In this case I would write:so the answer is -3t^{-1.6}?

\(\displaystyle \frac{d}{dt}\left(5t^{-\frac{3}{5}} \right)=5 \left(- \frac{3}{5} \right)t^{-\frac{3}{5}-1}=-3t^{-\frac{8}{5}}\)