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Beliebt Rechnen >

(\partial)/(\partial y)(xarctan(x+2y))

Lösung

\frac{\partial}{\partial y} (x arctan (x + 2 y))

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial y} (x arctan (x + 2 y))

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{\partial}{\partial y} (arctan (x + 2 y))

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial y} (x + 2 y) = 2

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

Vereinfache

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

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

Beliebte Beispiele

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

d er i v a t i v e e^{x} - e^{- x} - 2 x

integral of 2x(x^2+1)^{-6}

\int 2 x (x^{2} + 1)^{- 6} d x

derivative f(t)= 1/((t^2+3t+1)^{5/2)}

d er i v a t i v e f (t) = \frac{1}{( t ^{2} + 3 t + 1 ) ^{\frac{5}{2}}}

integral of sqrt(1-e^x)

\int 1 - e^{x} d x

limit as x approaches-infinity of x^3-x

x \to - \infty lim (x^{3} - x)