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

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d}{d x} ((4 x^{2} + 1)^{2})

\int \frac{1}{x ^{4} ( x ^{2} + 3 ) ^{\frac{1}{2}}} d x

x \to 0 + lim (e^{\frac{5}{x}})

\frac{d}{d x} ((x^{8} - 2)^{3})

\frac{\partial}{\partial x} (4 y^{3} + 2 x^{2} y + 1)