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

Lösung

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

n = 0 \sum \infty \frac{5 n}{2 n - 1}

y^{^{'}} + 3 y = e^{- 3 x}

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

\frac{\partial}{\partial x} (x^{9} y z^{2} + 9 yz)

\int \frac{1}{1 + 2 u} d u