en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 1/(9x+1)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of sin^2(x/3)

\int sin^{2} (\frac{x}{3}) d x

derivative of-2x+1/x

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

integral of (5x^2+5x-4)

\int (5 x^{2} + 5 x - 4) d x

derivative of xcos(x^2)derivative of

x cos (x^{2})

derivative of (x+6/(5x^2e^x))

\frac{d}{d x} (\frac{x + 6}{5 x ^{2} e ^{x}})

Frequently Asked Questions (FAQ)

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