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Beliebt Rechnen >

(\partial)/(\partial x)(9xarctan(x/y))

Lösung

\frac{\partial}{\partial x} (9 x arctan (\frac{x}{y}))

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} (9 x arctan (\frac{x}{y}))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 9 \frac{\partial}{\partial x} (x arctan (\frac{x}{y}))

Wende die Produktregel an:

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

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

= 9 (\frac{\partial}{\partial x} (x) arctan (\frac{x}{y}) + \frac{\partial}{\partial x} (arctan (\frac{x}{y})) x)

\frac{\partial}{\partial x} (x) = 1

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

= 9 (1 \cdot arctan (\frac{x}{y}) + \frac{y}{x ^{2} + y ^{2}} x)

Vereinfache

9 (1 \cdot arctan (\frac{x}{y}) + \frac{y}{x ^{2} + y ^{2}} x) : 9 (arctan (\frac{x}{y}) + \frac{x y}{x ^{2} + y ^{2}})

= 9 (arctan (\frac{x}{y}) + \frac{x y}{x ^{2} + y ^{2}})

Beliebte Beispiele

y=e^{-x}sin(pi)x

y = e^{- x} sin (π) x

limit as x approaches 1 of {3f(x)-2h(x)}

x \to 1 lim ({3 f (x) - 2 h (x)})

limit as x approaches 0 of (cos(3x))/(x+3)

x \to 0 lim (\frac{cos ( 3 x )}{x + 3})

derivative of (x+1^{-2})

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

y^{''}+4y^'+5y=5x+5e^{-x}

y^{^{''}} + 4 y^{^{'}} + 5 y = 5 x + 5 e^{- x}