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Beliebt Rechnen >

(\partial)/(\partial x)(3xln(y)+yln(z)-2x)

Lösung

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

Lösung

3 ln (y) - 2

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (3 x ln (y)) = 3 ln (y)

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

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

= 3 ln (y) + 0 - 2

Vereinfache

= 3 ln (y) - 2

Beliebte Beispiele

integral of sqrt(x)(x+1/x)

\int x (x + \frac{1}{x}) d x

integral of x^2

\int x^{2} d x

limit as x approaches 0+of (2x)/(|x|)

x \to 0 + lim (\frac{2 x}{∣ x ∣})

derivative of sqrt(x)(x^2-1)

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

derivative of sqrt((x+2^2*(x^2)/2))

\frac{d}{d x} ((x + 2)^{2} \cdot \frac{x ^{2}}{2})