derivative of x^3+ax^2y+bxy^2+y^3

Lösung

\frac{d}{d x} (x^{3} + a x^{2} y + b x y^{2} + y^{3})

3 x^{2} + a (2 x y + \frac{d y}{d x} x^{2}) + b (y^{2} + 2 x y \frac{d y}{d x}) + 3 y^{2} \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} (x^{3} + a x^{2} y + b x y^{2} + y^{3})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (a x^{2} y) + \frac{d}{d x} (b x y^{2}) + \frac{d}{d x} (y^{3})

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

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

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

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

= 3 x^{2} + a (2 x y + \frac{d y}{d x} x^{2}) + b (y^{2} + 2 x y \frac{d y}{d x}) + 3 y^{2} \frac{d y}{d x}

\int e^{0.5 t} d t

x \to 2 lim (\frac{( 3 x - 6 )}{1 - 4 x - 7})

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

\int 8 cos (x) d x

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 3 y = 2 x - 17