(\partial)/(\partial x)((z)(x^2ln(y)-z))

Lösung

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

2 z x ln (y)

Schritte zur Lösung

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

Behandle

z, y

als Konstanten

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (x^{2} ln (y)) = 2 x ln (y)

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

= z (2 x ln (y) - 0)

Vereinfache

= 2 z x ln (y)

e x p an d (a - 1, b) (a + 1, b + 1)

e x p an d \frac{2 - 14 x ^{\frac{12}{7}}}{7 x ^{\frac{5}{7}}}

e x p an d 2 e^{- x} x - e^{- x} (x^{2} - 17)

e x p an d (t - 2) cos (2 π t)

e x p an d 2 e^{- x} x - e^{- x} (x^{2} - 16)