What is the derivative of e^{i2x} ?

The derivative of e^{i2x} is -sin(2x)*2+icos(2x)*2

What is the first derivative of e^{i2x} ?

The first derivative of e^{i2x} is -sin(2x)*2+icos(2x)*2

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

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

Solution steps

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

Simplify

e^{i 2 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^{i2x} ?
The derivative of e^{i2x} is -sin(2x)*2+icos(2x)*2
What is the first derivative of e^{i2x} ?
The first derivative of e^{i2x} is -sin(2x)*2+icos(2x)*2