Differentiating f(t) with Chain Rule

[helpm3pl3ase]

f(t) = (1+tan t)^(1/3) differentiate using chain rule.

u = 1 + tan t
y = u^(1/3)

dy/dt = dy/du x du/dt


u=1+tan t

1/3 u^(-2/3) when u = 1 + tan t x sec^(2)t =

= sec^(2)t/3(1+tan t)^(2/3)

Did I do this correct??

 

[courtrigrad]

$$f(t) = (1+ \tan t)^{\frac{1}{3}}$$.

$$\frac{du}{dt} = sec^{2} t$$

So it should be $$\frac{1}{3}(1+ \tan t)^{-\frac{2}{3}}\sec^{2}t$$

 

[Karlisbad]

and How does it apply whenever we have the fractional derivtive operator $$D^{q}f(g(x))$$ (1)

If we wish to calculate the derivative of (1) respect to x, q>0 and real