If #g(5) = -3, g'(5) = 6, h(5) = 3, h'(5) = -2# what is #f'(5)#, if #f(x)=g(h(x))#. Is it possible to find it?
1 Answer
Jun 14, 2016
The trick here is to use the chain rule. In words, the chain rule states that the derivative of a composite function like
Expressed mathematically, if
#f(x)=g(h(x))#
then
#f'(x)=g'(h(x))*h'(x)#
Thus,
#f'(5)=g'(h(5))*h'(5)#
We know that
#f'(5)=g'(3)*(-2)#
However, we do not know the value of