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

Lösung

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

z (2 x y + y^{2} z)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= z (2 x y + y^{2} z)

e x p an d \frac{2 x ( 4 x ^{3} + x ^{2} + 1 ) + 3}{3 x + 15}

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

e x p an d e^{3 x^{2} + x} (6 x + 1)

e x p an d \frac{3 ( x ^{2} + 2 ) ^{\frac{4}{3}} + 3}{2 ( x ^{2} + 2 ) ^{\frac{1}{3}}}

e x p an d (3 - 5 x e^{x}) (3 x + 2)