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## Homework Statement

using mathematical induction, show that

d^n/dx^n(lnx)= (-1)^(n-1)*((n-1)!/x^n)

## Homework Equations

## The Attempt at a Solution

basis step:

for n=1 we get d/dx(lnx)=(-1)^0*((0)!/x^1)

which gives d/dx(lnx)=1/x

inductive step:

assuming it holds for all n, d^n/dx^n=(-1)^(n-1)*((n-1)!/x^n)

for n+1, d^(n+1)/dx^(n+1)=(-1)^n*(n!/x^(n+1))

d/dx[d^n/dx^n(lnx)]=d/dx((-1)^(n-1)*((n-1)!/x^n))

=-((n(n-1)!x^(n-1))/x^(2n))(-1)^(n-1)

=(-1)^n*(n!*x^(-n-1))

=(-1)^n*(n!/x^(n+1)

any help would be greatly appreciated, and sorry if its a bit hard to read, hopefully ill be posting using latex soon