I'm not sure if I'm simply forgetting basics here...

what is dy/dx where y=

x^(x*r/k)

r and k are constants.

y=x^(x*r/k)
Take natural logarithms of each side:
LNy=LN(x^(x*r/k)).
Recall the rule for exponents within the logarithm function:
LNy=(x*r/k)LN(x).
Now take derivatives of both sides:
(1/y)(dy/dx)=...

Can you finish it from here? Remember to substitute the original expression for y into the (1/y) term.

That's a nice way of doing it,
I will be right from here.

Thanks a heap :)