derivative of 7xy

Lösung

\frac{d}{d x} (7 x y)

7 (y + x \frac{d y}{d x})

Schritte zur Lösung

\frac{d}{d x} (7 x y)

Entferne die Konstante:

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

= 7 \frac{d}{d x} (x y)

Wende die Produktregel an:

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

f = x, g = y

= 7 (\frac{d x}{d x} y + \frac{d y}{d x} x)

\frac{d x}{d x} = 1

= 7 (1 \cdot y + \frac{d y}{d x} x)

Vereinfache

= 7 (y + x \frac{d y}{d x})

\frac{d}{d x} (arcsec (2 x + 1))

\int_{1}^{9} \frac{x - 1}{x} d x

x \to 2 lim (3 x^{2} - 4 x + 2)

\int (u + 4) (2 u + 1) d u

y^{^{''}} - 2 y^{^{'}} + 2 y = cos (t), y (0) = 1, y^{^{'}} (0) = 0