en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 + 2 x^{2}) = 4 x

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

Simplify

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

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

Popular Examples

derivative of x^{2/3}*(x-4^2)

\frac{d}{d x} (x^{\frac{2}{3}} \cdot (x - 4)^{2})

derivative of (x^2/(a^2)+(y^2)/(b^2))

\frac{d}{d x} (\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}})

integral of (x(sin(x^2)))(cos^8(x^2))

\int (x (sin (x^{2}))) (cos^{8} (x^{2})) d x

derivative of 81cos(3x)

\frac{d}{d x} (81 cos (3 x))

(\partial)/(\partial x)(x^3-6x^2-34x+40)

\frac{\partial}{\partial x} (x^{3} - 6 x^{2} - 34 x + 40)

Frequently Asked Questions (FAQ)

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