derivative of-2xsin(2x)

Lösung

\frac{d}{d x} (- 2 x sin (2 x))

- 2 (sin (2 x) + 2 x cos (2 x))

Schritte zur Lösung

\frac{d}{d x} (- 2 x sin (2 x))

Entferne die Konstante:

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

= - 2 \frac{d}{d x} (x sin (2 x))

Wende die Produktregel an:

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

f = x, g = sin (2 x)

= - 2 (\frac{d x}{d x} sin (2 x) + \frac{d}{d x} (sin (2 x)) x)

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

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

= - 2 (1 \cdot sin (2 x) + cos (2 x) \cdot 2 x)

Vereinfache

= - 2 (sin (2 x) + 2 x cos (2 x))

d er i v a t i v e f (t) = cos (t)

\frac{\partial}{\partial x} (x^{2} y^{3} + 4 x yz - 3 yz)

l a pl a ce t r an s f or m 6 e^{- 3} - t^{2} + 2 t - 8

x y^{^{'}} + 2 y = - 2 sin (x)

\int 10 sin^{3} (x co) s^{7} x d x