derivative of 3x^3y

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{3}, g = y

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

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

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

\int_{0}^{3} \frac{1}{x} d x

\int_{0}^{t} x e^{- x} d x

x y^{^{'}} - y = 2 x^{2} - 2 x - 2

x y^{^{'}} - y = x, y (1) = 10

\int_{0}^{2} π (3 x^{2})^{2} d x