What is d/dx(cot^-1(x^2))?

Chain Rule, Log Differentiation & Rate of Change · Question 33 of 130

Question 33

EasyOriginal question

What is $\frac{d}{dx}\left(\cot^{-1}(x^{2})\right)$ ?

\frac{2x}{1 + x^{4}}

Correct answerYour answer

-\frac{1}{1 + x^{4}}

Correct answerYour answer

-\frac{2x}{1 + x^{2}}

Correct answerYour answer

-\frac{2x}{1 + x^{4}}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$\frac{d}{dx}\cot^{-1} u = -\frac{u'}{1 + u^{2}}$ with $u = x^{2}$ , $u' = 2x$ .
$-\frac{2x}{1 + x^{4}}$ .

Worth noting

$\frac{2x}{1 + x^{4}}$ is the derivative of $\tan^{-1}(x^{2})$ ; $\cot^{-1}$ carries a minus sign.

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

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