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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

integral of (2x+1)/(x^2+x-2)

\int \frac{2 x + 1}{x ^{2} + x - 2} d x

derivative of x/(y^2+x^2)

\frac{d}{d x} (\frac{x}{y ^{2} + x ^{2}})

integral of x/(sqrt(-x^2+4x+4))

\int \frac{x}{- x ^{2} + 4 x + 4} d x

limit as x approaches infinity of (4^{x+1}+2^x)/(4^x)

x \to \infty lim (\frac{4 ^{x + 1} + 2 ^{x}}{4 ^{x}})

derivative of-7ln(5x^2-11)

\frac{d}{d x} (- 7 ln (5 x^{2} - 11))