(\partial)/(\partial x)((x^2+y^2)e^{-y})

Lösung

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

2 e^{- y} x

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (y^{2}) = 0

= e^{- y} (2 x + 0)

Vereinfache

= 2 e^{- y} x

y^{^{'}} = \frac{2 x y}{x ^{2} - y ^{2}}, y (1) = 1

d er i v a t i v e y = (x^{5} + 1)^{8}

\int 2 x + 2 x^{- 2} d x

\int \frac{x}{6 + π} d x

\frac{d}{d x} ((x^{2}) \cdot ln (x))