(\partial)/(\partial x)(3xe^{x^2+y^2})

Lösung

\frac{\partial}{\partial x} (3 x e^{x^{2} + y^{2}})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x e^{x^{2} + y^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 3 \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}}

= 3 (\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

= 3 (1 \cdot e^{x^{2} + y^{2}} + e^{x^{2} + y^{2}} \cdot 2 xx)

Vereinfache

3 (1 \cdot e^{x^{2} + y^{2}} + e^{x^{2} + y^{2}} \cdot 2 xx) : 3 (e^{x^{2} + y^{2}} + 2 e^{x^{2} + y^{2}} x^{2})

= 3 (e^{x^{2} + y^{2}} + 2 e^{x^{2} + y^{2}} x^{2})

\int \frac{cos ( x )}{sin ^{2} ( x ) - 49} d x

\frac{d}{d x} (tan^{2} (x^{2} - 5 x))

x \to 0 lim (\frac{8}{6 + e ^{x}})

d er i v a t i v e 0.5 cos (2 π t)

\frac{\partial}{\partial x} (4 x y^{3} + 1)