Differentiate the following. (a) y = sin(x4) (b) y = sin*(x) Solution (a) If y = sin(x*), then the outer function is the sine function and the inner function is the power function, so the Chain Rule gives the following. dy d sin COS dx dx ( x4) ( x4) outer evaluated derivative evaluated derivative function at inner of outer at inner of inner function function function function (b) Note that sin (x) = (sin(x)) Here the outer function is the power function and the inner function is the sine function. So dy d dx dx (sin(x)) 4 = 4 . (sin(x)) 3 inner derivative of outer derivative function function evaluated of inner at inner function function