(\partial)/(\partial x)(xy^2-2y^3+3xz)

Lösung

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

y^{2} + 3 z

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x y^{2}) - \frac{\partial}{\partial x} (2 y^{3}) + \frac{\partial}{\partial x} (3 x z)

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

\frac{\partial}{\partial x} (2 y^{3}) = 0

\frac{\partial}{\partial x} (3 x z) = 3 z

= y^{2} - 0 + 3 z

Vereinfache

= y^{2} + 3 z

n = 0 \sum \infty \frac{n !}{n ^{3}}

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

\frac{d}{d x} (sin (x - 2))

\frac{d}{d x} (\frac{( 4 x - 4 ) ^{5}}{( 2 x - 5 ) ^{7}})

d er i v a t i v e 38 e^{x^{2}} x