en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of arctan(1/(x^2))

Solution

\frac{d}{d x} (arctan (\frac{1}{x ^{2}}))

Solution

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

Solution steps

\frac{d}{d x} (arctan (\frac{1}{x ^{2}}))

Apply the chain rule:

\frac{1}{( \frac{1}{x ^{2}} ) ^{2} + 1} \frac{d}{d x} (\frac{1}{x ^{2}})

= \frac{1}{( \frac{1}{x ^{2}} ) ^{2} + 1} \frac{d}{d x} (\frac{1}{x ^{2}})

\frac{d}{d x} (\frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

= \frac{1}{( \frac{1}{x ^{2}} ) ^{2} + 1} (- \frac{2}{x ^{3}})

Simplify

\frac{1}{( \frac{1}{x ^{2}} ) ^{2} + 1} (- \frac{2}{x ^{3}}) : - \frac{2 x}{1 + x ^{4}}

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

Popular Examples

(\partial)/(\partial x)(8x^2-16y^3)

\frac{\partial}{\partial x} (8 x^{2} - 16 y^{3})

limit as x approaches 0 of 1+sin(x^2)

x \to 0 lim (1 + sin (x^{2}))

integral of (-4+tan^2(x))

\int (- 4 + tan^{2} (x)) d x

(\partial)/(\partial x)(e^{3x+4y})

\frac{\partial}{\partial x} (e^{3 x + 4 y})

integral of (6sin(x))

\int (6 sin (x)) d x

Frequently Asked Questions (FAQ)

What is the derivative of arctan(1/(x^2)) ?
The derivative of arctan(1/(x^2)) is -(2x)/(1+x^4)
What is the first derivative of arctan(1/(x^2)) ?
The first derivative of arctan(1/(x^2)) is -(2x)/(1+x^4)