Trouble taking the derivative. Hung up on the algebra

I don't know if I should post this here or on the algebra forum.

Trying to find the derivative of f (X) = ³√t (t² + 4)

Let ³√t be a

Let (t² + 4) be b

f(X)' = a'b +b'a

a' =⅓t٨-⅔

b' = 2t

thus f(x)' =(⅓t٨-⅔)(t² + 4) + 2t ³√t

or (t²+4/3t٨⅔) +2t*t٨⅓

I do not understand how to get from here to the answer (7t+4)/(3t٨⅔)

Thanks for any help or advice.

Re: Trouble taking the derivative. Hung up on the algebra

distribute ...

take the derivative w/r to t using the power rule ...

common denominator is ...

Re: Trouble taking the derivative. Hung up on the algebra

Thank you for the help. Evidently, the fundamental problem is that I do not understand dealing with these fractional powers. I have searched it on the web and gained some knowledge, but why t⅓ X t² is t٨7/3 alludes me. Can you explain or direct me to an explanation? Also, where do you find the fonts to write out this math so elegantly? (At 71, I am finding it a struggle to re-tool in math, so I can go on an learn some calculus!)

Re: Trouble taking the derivative. Hung up on the algebra

you should already know the fundamental rule that