Consider , where is a constant and . For which value of does for all…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Consider

F(x)=k\ln|x|-\dfrac{1}{x}+C

, where

k

is a constant and

x\ne 0

. For which value of

k

does

F'(x)=\dfrac{1}{x^{2}}

for all

x\ne 0

? (a)

k=2

(b)

k=1

(c)

k=0

(d)

k=-1

Related theory

Differentiation Rules
Advanced Differentiation
Derivatives of standard functions via chain rule
Exponential and logarithmic functions
Continuity and Differentiability

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