Question

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

Answer 1

`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`