en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 1/(5x-1)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of arcsin(x^4)derivative of

arcsin (x^{4})

derivative of f(x)= 7/x derivative of

f (x) = \frac{7}{x}

limit as x approaches infinity of ((x-3)/(x-4))^{-x}

x \to \infty lim ((\frac{x - 3}{x - 4})^{- x})

derivative of ln(sinh(5x))

\frac{d}{d x} (ln (sinh (5 x)))

derivative of y=(3x-2x^2)^3 derivative of

y = (3 x - 2 x^{2})^{3}

Frequently Asked Questions (FAQ)

What is the derivative of 1/(5x-1) ?
The derivative of 1/(5x-1) is -5/((5x-1)^2)
What is the first derivative of 1/(5x-1) ?
The first derivative of 1/(5x-1) is -5/((5x-1)^2)