What is the derivative of (11x)/((2+x^2)) ?

The derivative of (11x)/((2+x^2)) is (11(2-x^2))/((2+x^2)^2)

What is the first derivative of (11x)/((2+x^2)) ?

The first derivative of (11x)/((2+x^2)) is (11(2-x^2))/((2+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{11 x}{( 2 + x ^{2} )}

\frac{11 ( 2 - x ^{2} )}{( 2 + x ^{2} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{11 x}{2 + x ^{2}})

Take the constant out:

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

= 11 \frac{d}{d x} (\frac{x}{2 + x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 11 \cdot \frac{\frac{d x}{d x} ( 2 + x ^{2} ) - \frac{d}{d x} ( 2 + x ^{2} ) x}{( 2 + x ^{2} ) ^{2}}

\frac{d x}{d x} = 1

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

= 11 \cdot \frac{1 \cdot ( 2 + x ^{2} ) - 2 xx}{( 2 + x ^{2} ) ^{2}}

Simplify

11 \cdot \frac{1 \cdot ( 2 + x ^{2} ) - 2 xx}{( 2 + x ^{2} ) ^{2}} : \frac{11 ( 2 - x ^{2} )}{( 2 + x ^{2} ) ^{2}}

= \frac{11 ( 2 - x ^{2} )}{( 2 + x ^{2} ) ^{2}}

x \to 2 lim (\frac{x + 1}{x - 1})

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

y^{^{'}} = \frac{y ^{2}}{x ^{2}}

y = arcsin (\frac{x + 1}{x - 1})

\frac{\partial}{\partial u} (ln (5 u^{2} + uv))

What is the derivative of (11x)/((2+x^2)) ?
The derivative of (11x)/((2+x^2)) is (11(2-x^2))/((2+x^2)^2)
What is the first derivative of (11x)/((2+x^2)) ?
The first derivative of (11x)/((2+x^2)) is (11(2-x^2))/((2+x^2)^2)