(\partial)/(\partial x)(7xcos(3xy))

Lösung

\frac{\partial}{\partial x} (7 x cos (3 x y))

7 (cos (3 x y) - 3 x y sin (3 x y))

Schritte zur Lösung

\frac{\partial}{\partial x} (7 x cos (3 x y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 7 \frac{\partial}{\partial x} (x cos (3 x y))

Wende die Produktregel an:

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

f = x, g = cos (3 x y)

= 7 (\frac{\partial}{\partial x} (x) cos (3 x y) + \frac{\partial}{\partial x} (cos (3 x y)) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (cos (3 x y)) = - sin (3 x y) \cdot 3 y

= 7 (1 \cdot cos (3 x y) + (- sin (3 x y) \cdot 3 y) x)

Vereinfache

= 7 (cos (3 x y) - 3 x y sin (3 x y))

\int \frac{12 x}{3 3 - x ^{2}} d x

(- 5)^{^{'}}

\int_{5}^{8} \frac{x}{x ^{2} + 4 x + 20} d x

x \to \infty lim (x + 2)

\frac{\partial}{\partial x} (x y + \frac{y}{x})