en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 1/((x^2+1)^4)

Solution

derivative of

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

Solution

- \frac{8 x}{( x ^{2} + 1 ) ^{5}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{4}{( x ^{2} + 1 ) ^{5}} \frac{d}{d x} (x^{2} + 1)

= - \frac{4}{( x ^{2} + 1 ) ^{5}} \frac{d}{d x} (x^{2} + 1)

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

= - \frac{4}{( x ^{2} + 1 ) ^{5}} \cdot 2 x

Simplify

- \frac{4}{( x ^{2} + 1 ) ^{5}} \cdot 2 x : - \frac{8 x}{( x ^{2} + 1 ) ^{5}}

= - \frac{8 x}{( x ^{2} + 1 ) ^{5}}

Popular Examples

(\partial)/(\partial z)(x^2y+y^2z)

\frac{\partial}{\partial z} (x^{2} y + y^{2} z)

sum from n=1 to infinity of n/(n(n+3))

n = 1 \sum \infty \frac{n}{n ( n + 3 )}

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

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

(dy)/(dx)=e^{2.3x-1.9y}

\frac{d y}{d x} = e^{2.3 x - 1.9 y}

integral of sec^4((3x)/2)tan^2((3x)/2)

\int sec^{4} (\frac{3 x}{2}) tan^{2} (\frac{3 x}{2}) d x

Frequently Asked Questions (FAQ)

What is the derivative of 1/((x^2+1)^4) ?
The derivative of 1/((x^2+1)^4) is -(8x)/((x^2+1)^5)
What is the first derivative of 1/((x^2+1)^4) ?
The first derivative of 1/((x^2+1)^4) is -(8x)/((x^2+1)^5)