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Derivatives & Second-Order Derivatives · Question 4 of 96

Question 4

EasyOriginal question

Differentiate log⁡(x2+4)\log\left(x^{2} + 4\right) with respect to xx.

Options for question 4

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. ddxlog⁡u=1ududx\frac{d}{dx}\log u = \frac{1}{u}\frac{du}{dx}, with u=x2+4u = x^{2} + 4.

  2. 1x2+4⋅2x=2xx2+4\frac{1}{x^{2} + 4} \cdot 2x = \frac{2x}{x^{2} + 4}.

Worth noting

1x2+4\frac{1}{x^{2} + 4} stops at the logarithm and leaves out the derivative of x2+4x^{2} + 4.

Concept
The chain rule with a logarithm
Typical time
60 s
Your time
—
The rule this testsThe rules of differentiation
Practise this chapter →

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.

Practise this chapter →

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.