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Popular >

derivative of e^{-2ix}

Solution

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

Solution

- 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

Popular Examples

(\partial)/(\partial x)((6x)/((x^2+9)))

\frac{\partial}{\partial x} (\frac{6 x}{( x ^{2} + 9 )})

sum from n=0 to infinity of n/(2^n)

n = 0 \sum \infty \frac{n}{2 ^{n}}

tangent of 9e^x+x tangent of

9 e^{x} + x

limit as x approaches-4 of (x^2-2)/(4-x)

x \to - 4 lim (\frac{x ^{2} - 2}{4 - x})

derivative of ln(5x^4)derivative of

ln (5 x^{4})

Frequently Asked Questions (FAQ)

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