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

Lösung

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

4 ln (y) - 4

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{\partial}{\partial x} (4 x) = 4

= 4 ln (y) + 0 - 4

Vereinfache

= 4 ln (y) - 4

\int \frac{x ^{2}}{x - 10} d x

\frac{d y}{d x} = (4 x + y)^{2}

\frac{d}{d x} (\frac{x ^{3} - 1}{x - 1})

\frac{\partial}{\partial x} (ln (10 x))

\frac{d}{d x} (\frac{x}{lo g _{e} ( x )})