MHB Find derivative of function with fractional exponent?

[coolbeans33]

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

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

 

[I like Serena]

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]

Re: find derivative of function with fractional exponent?

so the answer is -3t^-1.6?

 

[MarkFL]

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:

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