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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

integral of (2y)/(1+y^2)

\int \frac{2 y}{1 + y ^{2}} d y

integral of tanh(2x)ln(cosh(2x))

\int tanh (2 x) ln (cosh (2 x)) d x

fläche cos(x),x^2+2,[1,2]

a re a cos (x), x^{2} + 2, [1, 2]

integral of 5/(x(x^2+2)^2)

\int \frac{5}{x ( x ^{2} + 2 ) ^{2}} d x

inverselaplace s/(s^2+s)

in v erse l a pl a ce \frac{s}{s ^{2} + s}