en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 1/(8x-1)

Solution

\frac{d}{d x} (\frac{1}{8 x - 1})

Solution

- \frac{8}{( 8 x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{8 x - 1})

Apply exponent rule:

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

= \frac{d}{d x} ((8 x - 1)^{- 1})

Apply the chain rule:

- \frac{1}{( 8 x - 1 ) ^{2}} \frac{d}{d x} (8 x - 1)

= - \frac{1}{( 8 x - 1 ) ^{2}} \frac{d}{d x} (8 x - 1)

\frac{d}{d x} (8 x - 1) = 8

= - \frac{1}{( 8 x - 1 ) ^{2}} \cdot 8

Simplify

- \frac{1}{( 8 x - 1 ) ^{2}} \cdot 8 : - \frac{8}{( 8 x - 1 ) ^{2}}

= - \frac{8}{( 8 x - 1 ) ^{2}}

Popular Examples

integral of e^{5x+2}

\int e^{5 x + 2} d x

(\partial)/(\partial x)(cos^6(x^9y^3))

\frac{\partial}{\partial x} (cos^{6} (x^{9} y^{3}))

integral of sqrt(9+16x^2)

\int 9 + 16 x^{2} d x

(\partial)/(\partial x)((3x-2y)/(4x^2+y))

\frac{\partial}{\partial x} (\frac{3 x - 2 y}{4 x ^{2} + y})

integral from 0 to ln(5) of e^x

\int_{0}^{l n (5)} e^{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of 1/(8x-1) ?
The derivative of 1/(8x-1) is -8/((8x-1)^2)
What is the first derivative of 1/(8x-1) ?
The first derivative of 1/(8x-1) is -8/((8x-1)^2)