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Beliebt Rechnen >

(\partial)/(\partial z)(4xln(y)+yln(z)-x)

Lösung

\frac{\partial}{\partial z} (4 x ln (y) + y ln (z) - x)

Lösung

\frac{y}{z}

Schritte zur Lösung

\frac{\partial}{\partial z} (4 x ln (y) + y ln (z) - x)

Behandle

x, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial z} (4 x ln (y)) + \frac{\partial}{\partial z} (y ln (z)) - \frac{\partial}{\partial z} (x)

\frac{\partial}{\partial z} (4 x ln (y)) = 0

\frac{\partial}{\partial z} (y ln (z)) = \frac{y}{z}

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

= 0 + \frac{y}{z} - 0

Vereinfache

= \frac{y}{z}

Beliebte Beispiele

(x-4y-3)dx-(x-6y-5)dy=0

(x - 4 y - 3) d x - (x - 6 y - 5) d y = 0

limit as n approaches infinity of cos(n)

n \to \infty lim (cos (n))

limit as x approaches 0 of ((sin(9x)))/x

x \to 0 lim (\frac{( sin ( 9 x ) )}{x})

derivative f(x)=(x^2+9x+2)^5

d er i v a t i v e f (x) = (x^{2} + 9 x + 2)^{5}

tangent f(x)=2e^x+10x,\at x=0

t an g e n t f (x) = 2 e^{x} + 10 x, at x = 0