derivative of (1+sin(x)*cos(2x))

Lösung

\frac{d}{d x} ((1 + sin (x)) \cdot cos (2 x))

cos (x) cos (2 x) - 2 sin (2 x) (1 + sin (x))

Schritte zur Lösung

\frac{d}{d x} ((1 + sin (x)) cos (2 x))

Wende die Produktregel an:

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

f = 1 + sin (x), g = cos (2 x)

= \frac{d}{d x} (1 + sin (x)) cos (2 x) + \frac{d}{d x} (cos (2 x)) (1 + sin (x))

\frac{d}{d x} (1 + sin (x)) = cos (x)

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

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

Vereinfache

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

\int \frac{2 x ^{2} + 3 x + 7}{x ^{3} + 3 x} d x

\frac{d y}{d x} = (cos (x)) e^{y + s i n (x)}, y (0) = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = - \frac{1}{5}, y^{^{'}} (0) = - \frac{8}{5}

l a pl a ce t r an s f or m 3 e^{2 t} sin (4 t)

\frac{\partial}{\partial β} (sin (α) cos (β))