en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 1/((5+x^2))

Solution

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

Solution

- \frac{2}{( 5 + x ) ^{3}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{2}{( 5 + x ) ^{3}} \frac{d}{d x} (5 + x)

= - \frac{2}{( 5 + x ) ^{3}} \frac{d}{d x} (5 + x)

\frac{d}{d x} (5 + x) = 1

= - \frac{2}{( 5 + x ) ^{3}} \cdot 1

Simplify

= - \frac{2}{( 5 + x ) ^{3}}

Popular Examples

integral of 1/((t^2-1)^2)

\int \frac{1}{( t ^{2} - 1 ) ^{2}} d t

sum from n=1 to infinity of 4/(4n^2-1)

n = 1 \sum \infty \frac{4}{4 n ^{2} - 1}

(\partial)/(\partial x)(x^2yz^2-4cos(3yz))

\frac{\partial}{\partial x} (x^{2} y z^{2} - 4 cos (3 yz))

tangent of f(x)=-3x^2+1x,\at x=0 tangent of

f (x) = - 3 x^{2} + 1 x, at x = 0

derivative of 1+3sin^3(x)

\frac{d}{d x} (1 + 3 sin^{3} (x))

Frequently Asked Questions (FAQ)

What is the derivative of 1/((5+x^2)) ?
The derivative of 1/((5+x^2)) is -2/((5+x)^3)
What is the first derivative of 1/((5+x^2)) ?
The first derivative of 1/((5+x^2)) is -2/((5+x)^3)