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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

= 7 (e^{x^{2}} + 2 e^{x^{2}} x^{2}) + 0

Vereinfache

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

\int \frac{23}{( x ^{2} - 1 ) ^{2}} d x

n = 1 \sum \infty \frac{n - 1}{5 n - 1}

(x^{2} + 2 y^{^{'}}) y^{^{''}} + 2 x y^{^{'}} = 0

\frac{d}{d x} (\frac{3 + 8 x}{5 - 6 x})

\int (\frac{4}{x}) d x