(\partial)/(\partial x)(x^2+xe^2y-y)

Lösung

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

2 x + e^{2} y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 2 x + e^{2} y - 0

Vereinfache

= 2 x + e^{2} y

\frac{d}{d x} (\frac{( x + 1 ) ^{5}}{( 1 - x ) ^{4}})

d er i v a t i v e y = ln (e^{3 x})

x \to 49 lim (\frac{x ^{2}}{7} - \frac{7}{x})

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

t a y l or 3 x, 27