How do you use the chain rule to differentiate #(lnx)^10#?

1 Answer
Apr 1, 2018

#d/dx(lnx)^10=(10(lnx)^9)/x#

Explanation:

The Chain Rule tells us if we have a composition of functions #f(g(x)),# then #d/dx(f(g(x))=f'(g(x))*g'(x)#

The function in this problem is the composition of a logarithm and power. So, the Power Rule will be used to differentiate the power, and the fact that #d/dxlnx=1/x# to differentiate the logarithm.

#d/dx(lnx)^10=10(lnx)^9*d/dxlnx#

#d/dx(lnx)^10=(10(lnx)^9)/x#