(\partial)/(\partial x)(xz-5x^2y^3z^4)

Lösung

\frac{\partial}{\partial x} (x z - 5 x^{2} y^{3} z^{4})

z - 10 z^{4} y^{3} x

Schritte zur Lösung

\frac{\partial}{\partial x} (x z - 5 x^{2} y^{3} z^{4})

Behandle

z, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x z) - \frac{\partial}{\partial x} (5 x^{2} y^{3} z^{4})

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

\frac{\partial}{\partial x} (5 x^{2} y^{3} z^{4}) = 10 z^{4} y^{3} x

= z - 10 z^{4} y^{3} x

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

\int \frac{cos ( x )}{sin ^{2} ( x ) - 36} d x

y^{^{''}} + 2 y^{^{'}} + 122 y = 0

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

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