(\partial)/(\partial x)(x/(10)cos(5x))

Lösung

\frac{\partial}{\partial x} (\frac{x}{10} cos (5 x))

\frac{1}{10} (cos (5 x) - 5 x sin (5 x))

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x}{10} cos (5 x))

Entferne die Konstante:

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

= \frac{1}{10} \frac{\partial}{\partial x} (x cos (5 x))

Wende die Produktregel an:

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

f = x, g = cos (5 x)

= \frac{1}{10} (\frac{\partial}{\partial x} (x) cos (5 x) + \frac{\partial}{\partial x} (cos (5 x)) x)

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

\frac{\partial}{\partial x} (cos (5 x)) = - sin (5 x) \cdot 5

= \frac{1}{10} (1 \cdot cos (5 x) + (- sin (5 x) \cdot 5) x)

Vereinfache

= \frac{1}{10} (cos (5 x) - 5 x sin (5 x))

\int_{- 2}^{3} - x^{2} + x + 6 d x

\int (x + y)^{- 2} (x^{2} + 2 x y - y^{2}) d x

\int - \frac{e ^{4 x}}{x} d x

\frac{d}{d x} (cos (x) - \frac{1}{2} x)

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