(\partial)/(\partial x)((z)(y^2-3x^3y))

Lösung

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

- 9 zy x^{2}

Schritte zur Lösung

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

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (y^{2}) = 0

\frac{\partial}{\partial x} (3 x^{3} y) = 9 y x^{2}

= z (0 - 9 y x^{2})

Vereinfache

= - 9 zy x^{2}

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

e x p an d \frac{z ^{2}}{( z + 6 ) ( z + 9 )}

e x p an d A (1, - 2) B (5, - 5)

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

e x p an d \frac{( - 1 ) ^{n} n ( n - 1 ) x ^{n - 2}}{2 \cdot 5 ^{n + 1}}