Assertion (A): d/dxlog | x | = 1/x for every x ≠ 0. Reason (R): For x < 0, log | x | = log(-x), whose derivative is (-1)/(-x) = 1/x.

Question 62

MediumOriginal question

Assertion (A): $\frac{d}{dx}\log \lvert x \rvert = \frac{1}{x}$ for every $x \ne 0$ .
Reason (R): For $x < 0$ , $\log \lvert x \rvert = \log(-x)$ , whose derivative is $\frac{-1}{-x} = \frac{1}{x}$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

A is true: for $x > 0$ it is $\frac{1}{x}$ directly.
R is true and supplies the negative half, so it explains A.

Concept: The derivative of $\log \lvert x \rvert$
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsExponential and logarithmic functions

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Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.

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