(\partial)/(\partial x)(x^2+3yz+4xy)

Lösung

\frac{\partial}{\partial x} (x^{2} + 3 yz + 4 x y)

2 x + 4 y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} + 3 yz + 4 x y)

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (3 yz) + \frac{\partial}{\partial x} (4 x y)

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

\frac{\partial}{\partial x} (3 yz) = 0

\frac{\partial}{\partial x} (4 x y) = 4 y

= 2 x + 0 + 4 y

Vereinfache

= 2 x + 4 y

y^{^{'}} = (x y^{^{'}} + y) y^{1} 985

\frac{d}{d x} (\frac{2 x}{x ^{3}})

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

\int_{0}^{2} (x^{2})^{2} d x

x \to 0 lim (\frac{1}{1 - e ^{x}} - \frac{1}{x})