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

The derivative of (-1/((x-1)^2)) is 2/((x-1)^3)

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

The first derivative of (-1/((x-1)^2)) is 2/((x-1)^3)

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

\frac{2}{( x - 1 ) ^{3}}

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{2}{( x - 1 ) ^{3}} \frac{d}{d x} (x - 1)

= - \frac{2}{( x - 1 ) ^{3}} \frac{d}{d x} (x - 1)

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

= - (- \frac{2}{( x - 1 ) ^{3}} \cdot 1)

Simplify

= \frac{2}{( x - 1 ) ^{3}}

\frac{d y}{d t} - 2 t y = 12 t^{2} e^{t^{2}}

y^{^{'}} = (2 y^{2}) + x y^{2}

f^{^{'}} (x) = 2 x - \frac{3}{x ^{4}}

f (x) = \frac{2}{3 x + 1}

\int_{0}^{1} 7 e^{- 7 x} d x

What is the derivative of (-1/((x-1)^2)) ?
The derivative of (-1/((x-1)^2)) is 2/((x-1)^3)
What is the first derivative of (-1/((x-1)^2)) ?
The first derivative of (-1/((x-1)^2)) is 2/((x-1)^3)