What is the derivative of f(x)= 1/(5x-7) ?

The derivative of f(x)= 1/(5x-7) is -5/((5x-7)^2)

What is the first derivative of f(x)= 1/(5x-7) ?

The first derivative of f(x)= 1/(5x-7) is -5/((5x-7)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

f (x) = \frac{1}{5 x - 7}

- \frac{5}{( 5 x - 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{5 x - 7})

Apply exponent rule:

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

= \frac{d}{d x} ((5 x - 7)^{- 1})

Apply the chain rule:

- \frac{1}{( 5 x - 7 ) ^{2}} \frac{d}{d x} (5 x - 7)

= - \frac{1}{( 5 x - 7 ) ^{2}} \frac{d}{d x} (5 x - 7)

\frac{d}{d x} (5 x - 7) = 5

= - \frac{1}{( 5 x - 7 ) ^{2}} \cdot 5

Simplify

- \frac{1}{( 5 x - 7 ) ^{2}} \cdot 5 : - \frac{5}{( 5 x - 7 ) ^{2}}

= - \frac{5}{( 5 x - 7 ) ^{2}}

What is the derivative of f(x)= 1/(5x-7) ?
The derivative of f(x)= 1/(5x-7) is -5/((5x-7)^2)
What is the first derivative of f(x)= 1/(5x-7) ?
The first derivative of f(x)= 1/(5x-7) is -5/((5x-7)^2)