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Beliebt Rechnen >

d/(dy)((x^2+y^2)arctan(y/x))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2} + y^{2}, g = arctan (\frac{y}{x})

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

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

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

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

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

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

Beliebte Beispiele

integral of x/7

\int \frac{x}{7} d x

y^{^{'}} - 5 y = 10 x

inverselaplace 1/((s-4)^2)

in v erse l a pl a ce \frac{1}{( s - 4 ) ^{2}}

integral of 4/(25-x)

\int \frac{4}{25 - x} d x

derivative f(x)=294x^5-120x^4+420x^2

d er i v a t i v e f (x) = 294 x^{5} - 120 x^{4} + 420 x^{2}