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Beliebt Rechnen >

derivative y=(((x-2))/((x-3)))^2

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative f(x)=5x+3/x

d er i v a t i v e f (x) = 5 x + \frac{3}{x}

limit as x approaches a of 2x

x \to a lim (2 x)

integral from-infinity to 0 of xe^{2x}

\int_{- \infty}^{0} x e^{2 x} d x

y^{''}-y^'-6y=18cos(3x)

y^{^{''}} - y^{^{'}} - 6 y = 18 cos (3 x)

derivative f(x)=(3x)/((1-x)^2)

d er i v a t i v e f (x) = \frac{3 x}{( 1 - x ) ^{2}}