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

Lösung

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

2 x y^{3} + 3 y^{2} \frac{d y}{d x} x^{2} + 3 x^{2} y^{2} + 2 y \frac{d y}{d x} x^{3}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

\int \frac{3 - 3 x}{1 - x} d x

\frac{\partial}{\partial x} (6 \cdot x \cdot y + 2 \cdot y)

\frac{d}{d x} ((x - 1)^{4})

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

\int 144 - x^{2} d x