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Beliebt Rechnen >

derivative of (x+y^{1/2})

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x + y) = 1 + \frac{d y}{d x}

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

Vereinfache

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

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

Beliebte Beispiele

integral of 5xarctan(x)

\int 5 x arctan (x) d x

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

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

derivative of ln((x-1^3(x^2+1)^4))

\frac{d}{d x} (ln ((x - 1)^{3} (x^{2} + 1)^{4}))

derivative of 3x^2-e^{2x}

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

(dy}{dt}=-\frac{3y)/t-2-t^{-4}

\frac{d y}{d t} = - \frac{3 y}{t} - 2 - t^{- 4}