$\displaystyle f(x)= sin^4(x)$
What does 'u' in this situation equal?
$\displaystyle sin(x) $or$\displaystyle x^4$
$\displaystyle \frac{d}{dx} \tan{u} = \sec^2{u} \cdot \frac{du}{dx}
$
... in future, start a new problem with a new thread.
more examples of the chain rule ...
http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/chainruledirectory/ChainRule.html