Mathematics

Problem

Which of the following gives the general formula for the

n

th derivative of

p(x)=\ln x

for all integers

n\ge 1

? a)

p^{(n)}(x)=\dfrac{(-1)^{n}(n-1)!}{x^{n}}

p^{(n)}(x)=\dfrac{(-1)^{n-1}n!}{x^{n}}

p^{(n)}(x)=\dfrac{(-1)^{\,n-1}(n-1)!}{x^{n}}

p^{(n)}(x)=\dfrac{(-1)^{n-1}(n-1)!}{x^{\,n-1}}