(\partial)/(\partial x)(3xcos(4xy))

Lösung

\frac{\partial}{\partial x} (3 x cos (4 x y))

3 (cos (4 x y) - 4 x y sin (4 x y))

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x cos (4 x y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 3 \frac{\partial}{\partial x} (x cos (4 x y))

Wende die Produktregel an:

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

f = x, g = cos (4 x y)

= 3 (\frac{\partial}{\partial x} (x) cos (4 x y) + \frac{\partial}{\partial x} (cos (4 x y)) x)

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

\frac{\partial}{\partial x} (cos (4 x y)) = - sin (4 x y) \cdot 4 y

= 3 (1 \cdot cos (4 x y) + (- sin (4 x y) \cdot 4 y) x)

Vereinfache

= 3 (cos (4 x y) - 4 x y sin (4 x y))

\frac{\partial}{\partial x} (9 x e^{8 x y})

\int x (x + 1)^{8} d x

\frac{d y}{d x} + y = x e^{5 x} y^{6}

\int_{- 2}^{2} (x + 5) d x

y^{^{'}} y^{^{''}} = 1