What is the derivative of (3-x^2/(3+x^2)) ?

The derivative of (3-x^2/(3+x^2)) is -(12x)/((3+x^2)^2)

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

The first derivative of (3-x^2/(3+x^2)) is -(12x)/((3+x^2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

- \frac{12 x}{( 3 + x ^{2} ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 2 x ) ( 3 + x ^{2} ) - 2 x ( 3 - x ^{2} )}{( 3 + x ^{2} ) ^{2}} : - \frac{12 x}{( 3 + x ^{2} ) ^{2}}

= - \frac{12 x}{( 3 + x ^{2} ) ^{2}}

\frac{d y}{d x} = 6 y e^{x + 9}

x \to 0 lim ((1 - \frac{1}{x})^{x})

\int_{80}^{90} \frac{x - 80}{800} d x

x \to 1 lim (\frac{0}{x - 1})

(4 x + 3)^{4} (x + 1)^{- 3}

What is the derivative of (3-x^2/(3+x^2)) ?
The derivative of (3-x^2/(3+x^2)) is -(12x)/((3+x^2)^2)
What is the first derivative of (3-x^2/(3+x^2)) ?
The first derivative of (3-x^2/(3+x^2)) is -(12x)/((3+x^2)^2)