4.3 and 4.4 - The (all important) General Power Rule or Chain Rule
(A function h is a composite of functions f and g if h(x)  f [g(x)] . The domain of m is the set of all
numbers x such that x is in the domain of g, and g(x) is in the domain of f. )
Examples:
function
y  f (x) =  u(x)  n
(a)
derivative
y = f ( x) = n   u (x)  n 1  u( x)
(Notice that we now have a function raised
to a power and not just x raised to a power)
(b)
y = f ( x) = e u(x)
(c)
y = f (x) = ln u(x) , u(x)> 0
y = f ( x) = e u(x)  u( x)
y = f ( x) =
(Again, notice that we now have functions raised to a function and not just x )
Examples:
1
 u( x)
u (x)
4.3 HW # 1 – 35 (odd)
4.4 HW # 1 - 49 (every other odd), 51 - 61 (odd), 71