de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

d/(d{y)}(({z})(3{x}^2{y}^2+2{z}^2{x}{y}-2{z}{x}^3+4{z}{y}^3-4))

Lösung

\frac{d}{d y} ((z) (3 x^{2} y^{2} + 2 z^{2} x y - 2 z x^{3} + 4 z y^{3} - 4))

Lösung

z (2 z^{2} x + 12 y^{2} z + 6 x^{2} y)

Schritte zur Lösung

\frac{d}{d y} ((z) (3 x^{2} y^{2} + 2 z^{2} x y - 2 z x^{3} + 4 z y^{3} - 4))

Entferne die Konstante:

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

= z \frac{d}{d y} (3 x^{2} y^{2} + 2 z^{2} x y - 2 z x^{3} + 4 z y^{3} - 4)

Wende die Summen-/Differenzregel an:

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

= z (\frac{d}{d y} (3 x^{2} y^{2}) + \frac{d}{d y} (2 z^{2} x y) - \frac{d}{d y} (2 z x^{3}) + \frac{d}{d y} (4 z y^{3}) - \frac{d}{d y} (4))

\frac{d}{d y} (3 x^{2} y^{2}) = 6 y x^{2}

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

\frac{d}{d y} (2 z x^{3}) = 0

\frac{d}{d y} (4 z y^{3}) = 12 y^{2} z

\frac{d}{d y} (4) = 0

= z (6 y x^{2} + 2 z^{2} x - 0 + 12 y^{2} z - 0)

Vereinfache

= z (2 z^{2} x + 12 y^{2} z + 6 x^{2} y)

Beliebte Beispiele

erweitern e^{-x^2-y^2}(x^2+2y^2)

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

erweitern (6/D v+6/D w)^2

e x p an d (\frac{6}{D} v + \frac{6}{D} w)^{2}

erweitern (N-4)!

e x p an d (N - 4)!

erweitern ((x-u)/2)^2

e x p an d (\frac{x - u}{2})^{2}

erweitern (2s^3+10s+3)/(s^2(s+1)(s+2))

e x p an d \frac{2 s ^{3} + 10 s + 3}{s ^{2} ( s + 1 ) ( s + 2 )}