derivative of 5xsin(x)

Lösung

\frac{d}{d x} (5 x sin (x))

5 (sin (x) + x cos (x))

Schritte zur Lösung

\frac{d}{d x} (5 x sin (x))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x sin (x))

Wende die Produktregel an:

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

f = x, g = sin (x)

= 5 (\frac{d x}{d x} sin (x) + \frac{d}{d x} (sin (x)) x)

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

\frac{d}{d x} (sin (x)) = cos (x)

= 5 (1 \cdot sin (x) + cos (x) x)

Vereinfache

= 5 (sin (x) + x cos (x))

d er i v a t i v e 3 x - 2

\frac{d}{d x} (3 x^{2} - 2 x + 4)

\frac{\partial}{\partial y} (y (1 - x^{2}))

x \to 1 lim (\frac{2 x + 3}{x + 1})

\frac{\partial}{\partial y} (166 x + 456 y - \frac{5000}{x} - \frac{1080}{y} + 43590)