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Popular >

derivative of-1/((x-1^2))

Solution

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

Solution

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

Solution steps

\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}}

Popular Examples

integral from 0 to 5 of 4e^{2x}

\int_{0}^{5} 4 e^{2 x} d x

derivative of (x^2+x^3e^{-1/x})

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

integral of (6e^{1/x})/(x^2)

\int \frac{6 e ^{\frac{1}{x}}}{x ^{2}} d x

integral from 0 to pi of 2sin(x)+sin(2x)

\int_{0}^{π} 2 sin (x) + sin (2 x) d x

limit as t approaches 3 of (t^2)/(9-t^2)

t \to 3 lim (\frac{t ^{2}}{9 - t ^{2}})

Frequently Asked Questions (FAQ)

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)