(\partial)/(\partial x)((y)(3x^2+y^2)^3)

Lösung

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

18 y x (3 x^{2} + y^{2})^{2}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

= y \cdot 3 (3 x^{2} + y^{2})^{2} \cdot 6 x

Vereinfache

= 18 y x (3 x^{2} + y^{2})^{2}

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

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

e x p an d (e - 3 x) d x

e x p an d (x - 6) (x + 3)^{'}

e x p an d (8 + k) (x - 0, y - 2)