What is the derivative of 9/(x^2+5) ?

The derivative of 9/(x^2+5) is -(18x)/((x^2+5)^2)

What is the first derivative of 9/(x^2+5) ?

The first derivative of 9/(x^2+5) is -(18x)/((x^2+5)^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{9}{x ^{2} + 5})

- \frac{18 x}{( x ^{2} + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{9}{x ^{2} + 5})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{1}{x ^{2} + 5})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 9 \frac{d}{d x} ((x^{2} + 5)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{2} + 5 ) ^{2}} \frac{d}{d x} (x^{2} + 5)

= - \frac{1}{( x ^{2} + 5 ) ^{2}} \frac{d}{d x} (x^{2} + 5)

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

= 9 (- \frac{1}{( x ^{2} + 5 ) ^{2}} \cdot 2 x)

Simplify

9 (- \frac{1}{( x ^{2} + 5 ) ^{2}} \cdot 2 x) : - \frac{18 x}{( x ^{2} + 5 ) ^{2}}

= - \frac{18 x}{( x ^{2} + 5 ) ^{2}}

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

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

y = \frac{C}{x}

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

- y

What is the derivative of 9/(x^2+5) ?
The derivative of 9/(x^2+5) is -(18x)/((x^2+5)^2)
What is the first derivative of 9/(x^2+5) ?
The first derivative of 9/(x^2+5) is -(18x)/((x^2+5)^2)