(\partial)/(\partial x)(xy-z^2+17x^2z)

Lösung

\frac{\partial}{\partial x} (x y - z^{2} + 17 x^{2} z)

34 x z + y

Schritte zur Lösung

\frac{\partial}{\partial x} (x y - z^{2} + 17 x^{2} z)

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} (z^{2}) + \frac{\partial}{\partial x} (17 x^{2} z)

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

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

\frac{\partial}{\partial x} (17 x^{2} z) = 34 z x

= y - 0 + 34 z x

Vereinfache

= 34 x z + y

t an g e n t y = - x^{2} + 4 x + 2, (3, 5)

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

\frac{\partial}{\partial x} (4 x sin (6 x^{2} y))

\frac{d y}{d x} = x y - x

y^{^{''}} + 2 y^{^{'}} - 3 y = 0