Which of the following gives the general formula for the th derivative of for all…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Which of the following gives the general formula for the nnth derivative of p(x)=ln⁡xp(x)=\ln x for all integers n≥1n\ge 1? (a) p(n)(x)=(−1)n(n−1)!xnp^{(n)}(x)=\dfrac{(-1)^{n}(n-1)!}{x^{n}} (b) p(n)(x)=(−1)n−1n!xnp^{(n)}(x)=\dfrac{(-1)^{n-1}n!}{x^{n}} (c) p(n)(x)=(−1) n−1(n−1)!xnp^{(n)}(x)=\dfrac{(-1)^{\,n-1}(n-1)!}{x^{n}} (d) p(n)(x)=(−1)n−1(n−1)!x n−1p^{(n)}(x)=\dfrac{(-1)^{n-1}(n-1)!}{x^{\,n-1}}

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