What is the derivative of 5/(1+x^2) ?

The derivative of 5/(1+x^2) is -(10x)/((1+x^2)^2)

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

The first derivative of 5/(1+x^2) is -(10x)/((1+x^2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{5}{1 + x ^{2}}

- \frac{10 x}{( 1 + x ^{2} ) ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

5 (- \frac{1}{( 1 + x ^{2} ) ^{2}} \cdot 2 x) : - \frac{10 x}{( 1 + x ^{2} ) ^{2}}

= - \frac{10 x}{( 1 + x ^{2} ) ^{2}}

x = 2 3 y, x = 0, y = 7

\frac{( 2 s + 1 )}{s ^{2} + 2 s + 2}

\int - 5 sec^{2} (x) d x

f (x) = x^{3} - 25 x + 5, at x = 5

y^{^{'}} = \frac{( x ^{2} - y ^{2} )}{x y}, y (2) = 4

What is the derivative of 5/(1+x^2) ?
The derivative of 5/(1+x^2) is -(10x)/((1+x^2)^2)
What is the first derivative of 5/(1+x^2) ?
The first derivative of 5/(1+x^2) is -(10x)/((1+x^2)^2)