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Beliebt Rechnen >

derivative of sqrt((x-1/(x+1)))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

limit as x approaches 4 of (|3-x|)/(3-x)

x \to 4 lim (\frac{∣ 3 - x ∣}{3 - x})

integral from 0 to pi/4 of cos^2(x)

\int_{0}^{\frac{π}{4}} cos^{2} (x) d x

(\partial)/(\partial y)(4e^y)

\frac{\partial}{\partial y} (4 e^{y})

4y^{''}+7y^'-2y=0

4 y^{^{''}} + 7 y^{^{'}} - 2 y = 0

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

\int \frac{( x + 1 )}{x ^{2}} d x