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

The derivative of (-2/((x-1)^3)) is 6/((x-1)^4)

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

The first derivative of (-2/((x-1)^3)) is 6/((x-1)^4)

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

\frac{6}{( x - 1 ) ^{4}}

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{3}{( x - 1 ) ^{4}} \frac{d}{d x} (x - 1)

= - \frac{3}{( x - 1 ) ^{4}} \frac{d}{d x} (x - 1)

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

= - 2 (- \frac{3}{( x - 1 ) ^{4}} \cdot 1)

Simplify

- 2 (- \frac{3}{( x - 1 ) ^{4}} \cdot 1) : \frac{6}{( x - 1 ) ^{4}}

= \frac{6}{( x - 1 ) ^{4}}

\int (1 - 2 x)^{2021} d x

x \to + 4 + lim (ln (x - 4))

\frac{1}{( 1 - x ) ^{3}}, 0

\int \frac{2}{x + 2 + x} d x

e^{9}

What is the derivative of (-2/((x-1)^3)) ?
The derivative of (-2/((x-1)^3)) is 6/((x-1)^4)
What is the first derivative of (-2/((x-1)^3)) ?
The first derivative of (-2/((x-1)^3)) is 6/((x-1)^4)