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

Lösung

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

2 cos (4 x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

cos (2 x) \cdot 2 cos (2 x) + (- sin (2 x) \cdot 2) sin (2 x) : 2 cos (4 x)

= 2 cos (4 x)

\frac{\partial}{\partial x} (x^{0.9})

in v erse l a pl a ce \frac{1}{1 - L S}

\frac{d}{d x} (\frac{- 9}{x ^{2}})

\int e^{- 2 t} d t

y^{^{'}} - \frac{8}{x} y = \frac{y ^{4}}{x ^{17}}, y (1) = 1