derivative of e^{2x}-cos(2x)

解答

\frac{d}{d x} (e^{2 x} - cos (2 x))

2 e^{2 x} + 2 sin (2 x)

求解步骤

\frac{d}{d x} (e^{2 x} - cos (2 x))

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{2 x}) - \frac{d}{d x} (cos (2 x))

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

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

= e^{2 x} \cdot 2 - (- sin (2 x) \cdot 2)

化简

= 2 e^{2 x} + 2 sin (2 x)

x \to 0 lim (\frac{( sin ( 4 x ) )}{x})

x \to 0 lim (5 x)

t an g e n t f (x) = \frac{- 5}{x - 1}, at a = 8

t an g e n t r = 1 + cos (θ)

d er i v a t i v e g (x) = (2 x^{2} + x + 9)^{- 3}