(\partial)/(\partial x)(y+arctan(y/x))

Lösung

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

- \frac{y}{y ^{2} + x ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (y) = 0

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

= 0 - \frac{y}{y ^{2} + x ^{2}}

Vereinfache

= - \frac{y}{y ^{2} + x ^{2}}

\frac{\partial}{\partial y} (x^{3} - y^{2})

t a y l or ln (6 x + 1)

x \to \infty lim (\frac{e ^{5 x - 3}}{ln ( x - 2 )})

d er i v a t i v e f (x) = cos (a^{8} + x^{8})

\int_{0}^{\infty} x^{1} e^{- x} d x