Welcome to our community

Be a part of something great, join today!

Find derivative of function with fractional exponent?

coolbeans33

New member
Sep 19, 2013
23
I need to find the derivative of R(t)=5t-3/5

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

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,774
Re: find derivative of function with fractional exponent?

Welcome to MHB, coolbeans33! :)

I need to find the derivative of R(t)=5t-3/5

are there any derivative rules I can use for this problem?
Just the regular ones should do.
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 $\alpha$.
 

coolbeans33

New member
Sep 19, 2013
23
Re: find derivative of function with fractional exponent?

so the answer is -3t-1.6?
 
Last edited:

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Re: find derivative of function with fractional exponent?

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

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