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Chain Rule, Log Differentiation & Rate of Change · Question 54 of 130

Question 54

EasyOriginal question

What is ddx(log⁡(x2+1))\frac{d}{dx}\left(\log{\left(x^{2} + 1 \right)}\right)?

Options for question 54

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. ddxlog⁡u=u′u\frac{d}{dx}\log u = \frac{u'}{u} with u=x2+1u = x^{2} + 1.

  2. 2xx2+1\frac{2x}{x^{2} + 1}.

Worth noting

1x2+1\frac{1}{x^{2} + 1} stops before the derivative of the inside, 2x2x.

Concept
Exponential and logarithm inside a chain
Typical time
60 s
Your time
—
The rule this testsExponential and logarithmic functions
Practise this chapter →

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

Practise this chapter →

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