derivative of x^3y^2

Lösung

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

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

Schritte zur Lösung

\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}

= \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}

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

n \to \infty lim (\frac{n}{n})

n = 1 \sum \infty \frac{7}{n ^{2} + 36}

x \to 0 lim (∣ x ∣)

\int_{0}^{π} ∣ cos (x) ∣ d x

x \to 0 lim (- \frac{1}{1} + \frac{1}{x})