(\partial)/(\partial x)(7xe^{x^2+y^2})

Lösung

\frac{\partial}{\partial x} (7 x e^{x^{2} + y^{2}})

7 (e^{x^{2} + y^{2}} + 2 e^{x^{2} + y^{2}} x^{2})

Schritte zur Lösung

\frac{\partial}{\partial x} (7 x e^{x^{2} + y^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 7 \frac{\partial}{\partial x} (x e^{x^{2} + y^{2}})

Wende die Produktregel an:

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

f = x, g = e^{x^{2} + y^{2}}

= 7 (\frac{\partial}{\partial x} (x) e^{x^{2} + y^{2}} + \frac{\partial}{\partial x} (e^{x^{2} + y^{2}}) x)

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

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

= 7 (1 \cdot e^{x^{2} + y^{2}} + e^{x^{2} + y^{2}} \cdot 2 xx)

Vereinfache

7 (1 \cdot e^{x^{2} + y^{2}} + e^{x^{2} + y^{2}} \cdot 2 xx) : 7 (e^{x^{2} + y^{2}} + 2 e^{x^{2} + y^{2}} x^{2})

= 7 (e^{x^{2} + y^{2}} + 2 e^{x^{2} + y^{2}} x^{2})

\frac{\partial}{\partial z} (\frac{x ^{2} + z ^{2}}{y} + x yz + 5 x z^{2})

\int \frac{e ^{x} + 1}{e ^{x} - 1} d x

\frac{d}{d x} (\frac{1}{3 x})

\frac{\partial}{\partial x} (a sin (x) sin (y))

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