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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

t an g e n t f (x) = 3 x^{3} - x^{2} + 9, (2, 29)

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

in v erse l a pl a ce \frac{1}{( s ^{2} + 0.5 s + 1 )}

y^{^{''}} - 6 y^{^{'}} + 9 y = \frac{e ^{3 x}}{x ^{2}}

a re a x = 15 - y^{2}, x = y^{2} - 3