What is (\partial)/(\partial x)(1/(x-1)) ?

The answer to (\partial)/(\partial x)(1/(x-1)) is -1/((x-1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(1/(x-1))

\frac{\partial}{\partial x} (\frac{1}{x - 1})

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

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x - 1})

Apply exponent rule:

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

= \frac{\partial}{\partial x} ((x - 1)^{- 1})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x - 1) = 1

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

Simplify

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

\frac{\partial}{\partial x} (e^{\frac{x y}{z}})

\frac{e ^{x}}{cos ( x )}

\int sin (3 z) cos^{2} (3 z) d z

\int x sec^{2} (x^{2}) d x

What is (\partial)/(\partial x)(1/(x-1)) ?
The answer to (\partial)/(\partial x)(1/(x-1)) is -1/((x-1)^2)