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

Lösung

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

y + z^{3}

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= y + 0 + z^{3}

Vereinfache

= y + z^{3}

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

\int \frac{1}{( 6 x - 1 ) ^{2}} d x

\frac{d}{d x} (- 16 x^{2})

\frac{\partial}{\partial z} (9 z e^{x yz})

\frac{d}{d x} ((1 + cos (x)) sin (x))