d/(d{x)}(({z})(2{x}^2{y}+3{x}{z}+5{y}{z}^2-10))

Lösung

\frac{d}{d x} ((z) (2 x^{2} y + 3 x z + 5 y z^{2} - 10))

z (4 x y + 3 z)

Schritte zur Lösung

\frac{d}{d x} ((z) (2 x^{2} y + 3 x z + 5 y z^{2} - 10))

Entferne die Konstante:

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

= z \frac{d}{d x} (2 x^{2} y + 3 x z + 5 y z^{2} - 10)

Wende die Summen-/Differenzregel an:

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

= z (\frac{d}{d x} (2 x^{2} y) + \frac{d}{d x} (3 x z) + \frac{d}{d x} (5 y z^{2}) - \frac{d}{d x} (10))

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

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

\frac{d}{d x} (5 y z^{2}) = 0

\frac{d}{d x} (10) = 0

= z (4 x y + 3 z + 0 - 0)

Vereinfache

= z (4 x y + 3 z)

s im pl i f y (sin (x) + 1) (- sin (x))

s im pl i f y (x + (\frac{1}{x})) \cdot (1 + \frac{2}{x ^{2} - 1})

e x p an d e^{θ} (tan (θ) - θ)

e x p an d 2 m^{\frac{1}{3}} (3 m^{\frac{2}{3}} - m^{6})

s im pl i f y (3 - x) (2 - x)