What is the derivative of (3x/(9-x^2)) ?

The derivative of (3x/(9-x^2)) is (3(9+x^2))/((9-x^2)^2)

What is the first derivative of (3x/(9-x^2)) ?

The first derivative of (3x/(9-x^2)) is (3(9+x^2))/((9-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}{9 - x ^{2}})

\frac{3 ( 9 + x ^{2} )}{( 9 - x ^{2} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x}{9 - x ^{2}})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{x}{9 - x ^{2}})

Apply the Quotient Rule:

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

= 3 \cdot \frac{\frac{d x}{d x} ( 9 - x ^{2} ) - \frac{d}{d x} ( 9 - x ^{2} ) x}{( 9 - x ^{2} ) ^{2}}

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

\frac{d}{d x} (9 - x^{2}) = - 2 x

= 3 \cdot \frac{1 \cdot ( 9 - x ^{2} ) - ( - 2 x ) x}{( 9 - x ^{2} ) ^{2}}

Simplify

3 \cdot \frac{1 \cdot ( 9 - x ^{2} ) - ( - 2 x ) x}{( 9 - x ^{2} ) ^{2}} : \frac{3 ( 9 + x ^{2} )}{( 9 - x ^{2} ) ^{2}}

= \frac{3 ( 9 + x ^{2} )}{( 9 - x ^{2} ) ^{2}}

t^{3} - 3 t

x \to 3 lim (\frac{2}{x + 2})

\int_{0}^{\frac{π}{4}} 25 sin^{2} (x) d x

\frac{d}{d x} (\frac{3 ^{x}}{ln ( 3 )})

x \to 0 lim (\frac{x}{x ^{2} - 7 x + 1})

What is the derivative of (3x/(9-x^2)) ?
The derivative of (3x/(9-x^2)) is (3(9+x^2))/((9-x^2)^2)
What is the first derivative of (3x/(9-x^2)) ?
The first derivative of (3x/(9-x^2)) is (3(9+x^2))/((9-x^2)^2)