d/(d{x)}(({z})({x}{y}+{x}{z}^3-2{y}{z}))

Lösung

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

z (z^{3} + y)

Schritte zur Lösung

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

Entferne die Konstante:

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

= z \frac{d}{d x} (x y + x z^{3} - 2 y z)

Wende die Summen-/Differenzregel an:

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

= z (\frac{d}{d x} (x y) + \frac{d}{d x} (x z^{3}) - \frac{d}{d x} (2 y z))

\frac{d}{d x} (x y) = y

\frac{d}{d x} (x z^{3}) = z^{3}

\frac{d}{d x} (2 y z) = 0

= z (y + z^{3} - 0)

Vereinfache

= z (z^{3} + y)

e x p an d \frac{( x + 2 ) ^{\frac{1}{3}} - 2 ^{\frac{1}{3}}}{x}

e x p an d \frac{1}{( 1 + x + y + z ) ^{3}}

e x p an d \frac{ln ( x y ^{2} )}{( z )}

e x p an d f (x) (f (x) = 5 x + 6)

e x p an d y^{2} + (2 x + e^{y}) y y^{'} (x)