What is the derivative of f(x)=(2x)/(9x^2+1) ?

The derivative of f(x)=(2x)/(9x^2+1) is (2(-9x^2+1))/((9x^2+1)^2)

What is the first derivative of f(x)=(2x)/(9x^2+1) ?

The first derivative of f(x)=(2x)/(9x^2+1) is (2(-9x^2+1))/((9x^2+1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = \frac{2 x}{9 x ^{2} + 1}

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

Solution steps

\frac{d}{d x} (\frac{2 x}{9 x ^{2} + 1})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{x}{9 x ^{2} + 1})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (9 x^{2} + 1) = 18 x

= 2 \cdot \frac{1 \cdot ( 9 x ^{2} + 1 ) - 18 xx}{( 9 x ^{2} + 1 ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( 9 x ^{2} + 1 ) - 18 xx}{( 9 x ^{2} + 1 ) ^{2}} : \frac{2 ( - 9 x ^{2} + 1 )}{( 9 x ^{2} + 1 ) ^{2}}

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

\int_{4}^{7} x^{2} d x

\int y^{3} e^{y^{2}} d y

n = 5 \sum \infty \frac{9 ^{n}}{1 0 ^{n}}

\frac{d}{d x} (sin (x) - \frac{1}{3} sin^{3} (x))

\int - 25 sin (5 t - \frac{π}{2}) d t

What is the derivative of f(x)=(2x)/(9x^2+1) ?
The derivative of f(x)=(2x)/(9x^2+1) is (2(-9x^2+1))/((9x^2+1)^2)
What is the first derivative of f(x)=(2x)/(9x^2+1) ?
The first derivative of f(x)=(2x)/(9x^2+1) is (2(-9x^2+1))/((9x^2+1)^2)