derivative of 2x^3y^2

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = y^{2}

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

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

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

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

\frac{\partial}{\partial x} (cos (x))

d er i v a t i v e y = x (x - 2)^{3}

x \to \infty lim (\frac{3 x}{5})

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

\int_{- 1}^{1} e^{x} - (x^{2} - 1) d x