What is the derivative of (36x/((x^2+9)^2)) ?

The derivative of (36x/((x^2+9)^2)) is (108(-x^2+3))/((x^2+9)^3)

What is the first derivative of (36x/((x^2+9)^2)) ?

The first derivative of (36x/((x^2+9)^2)) is (108(-x^2+3))/((x^2+9)^3)

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{36 x}{( x ^{2} + 9 ) ^{2}})

\frac{108 ( - x ^{2} + 3 )}{( x ^{2} + 9 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{36 x}{( x ^{2} + 9 ) ^{2}})

Take the constant out:

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

= 36 \frac{d}{d x} (\frac{x}{( x ^{2} + 9 ) ^{2}})

Apply the Quotient Rule:

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

= 36 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 9 ) ^{2} - \frac{d}{d x} ( ( x ^{2} + 9 ) ^{2} ) x}{( ( x ^{2} + 9 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((x^{2} + 9)^{2}) = 4 x (x^{2} + 9)

= 36 \cdot \frac{1 \cdot ( x ^{2} + 9 ) ^{2} - 4 x ( x ^{2} + 9 ) x}{( ( x ^{2} + 9 ) ^{2} ) ^{2}}

Simplify

36 \cdot \frac{1 \cdot ( x ^{2} + 9 ) ^{2} - 4 x ( x ^{2} + 9 ) x}{( ( x ^{2} + 9 ) ^{2} ) ^{2}} : \frac{108 ( - x ^{2} + 3 )}{( x ^{2} + 9 ) ^{3}}

= \frac{108 ( - x ^{2} + 3 )}{( x ^{2} + 9 ) ^{3}}

\frac{d}{d x} (\frac{1}{5} cos (5 x))

\int_{1200}^{1204} 0.1 d x

\int 5 x^{\frac{1}{3}} + 2 x^{- \frac{1}{3}} + 11 d x

\int \frac{x + 1}{x ^{2} - 4 x + 8} d x

\int_{- 1}^{2} (2 - y^{2}) - (- y) d y

What is the derivative of (36x/((x^2+9)^2)) ?
The derivative of (36x/((x^2+9)^2)) is (108(-x^2+3))/((x^2+9)^3)
What is the first derivative of (36x/((x^2+9)^2)) ?
The first derivative of (36x/((x^2+9)^2)) is (108(-x^2+3))/((x^2+9)^3)