What is the derivative of e^{-2ix} ?

The derivative of e^{-2ix} is -sin(2x)*2-icos(2x)*2

What is the first derivative of e^{-2ix} ?

The first derivative of e^{-2ix} is -sin(2x)*2-icos(2x)*2

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

- sin (2 x) \cdot 2 - i cos (2 x) \cdot 2

Solution steps

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

Simplify

e^{- 2 i x} : cos (2 x) - i sin (2 x)

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

Apply the Sum/Difference Rule:

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

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

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

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

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

What is the derivative of e^{-2ix} ?
The derivative of e^{-2ix} is -sin(2x)*2-icos(2x)*2
What is the first derivative of e^{-2ix} ?
The first derivative of e^{-2ix} is -sin(2x)*2-icos(2x)*2