Derivative of (t - sqrt(t)) / t^(1 / 3).

Find the derivative of (t - sqrt(t)) / t^(1 / 3).

I got [4t^(1 / 3) - 3 + 2 / (t^(1 / 6))] / 6t^(7 / 3), which looks like:
http://www.wolframalpha.com/input/?i=%5B4t%5E%281+%2F+3%29+-+3+%2B+2+%2F+%28t%5E%281+%2F+6%29%29%5D+%2F+6t%5E%287+%2F+3%29
Is this correct?

f(t) = (t - √t) / t^(1/3) = t^(2/3) - t^(1/6)

f'(t) = (2/3)t^(-1/3) - (1/6)t^(-5/6)

You can do the algebra to check for equality.

why make this hard:

(t - t^(1/2)) / t^(1/3) = t^2/3 - t^(1/6). Now take derivatives.

f ( t ) = ( t - t^( 1 /2 ) ) / t^( 1 / 3 )
f ( t ) = t^(2 / 3 ) - t^(1 / 6 )
f ' ( t ) = ( 2 / 3)t^( - 1 / 3 ) - ( 1 / 6)t^( - 5 / 6 )

(t - t^(1/2))/t^(1/3) =
t^(2/3) - t^(1/6)
d/dt( t^(2/3) - t^(1/6) ) =
2t^(-1/3)/3 - t^(-5/6)/6