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Popular >

derivative of-ie^{-ix}

Solution

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

Solution

- cos (x) + i sin (x)

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= - cos (x) - (- i sin (x))

Simplify

= - cos (x) + i sin (x)

Graph

Popular Examples

limit as x approaches 3-of |(x-3)/(x-3)|

x \to 3 - lim (\frac{x - 3}{x - 3})

integral of 3/(x^2-8x+25)

\int \frac{3}{x ^{2} - 8 x + 25} d x

integral from 0 to 80 of (317)/(903*10)

\int_{0}^{80} \frac{317}{903 \cdot 10}

integral of (x^2)/(sqrt((1+x)))

\int \frac{x ^{2}}{( 1 + x )} d x

integral of 2/(x(x^2+4)^2)

\int \frac{2}{x ( x ^{2} + 4 ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of-ie^{-ix} ?
The derivative of-ie^{-ix} is -cos(x)+isin(x)
What is the first derivative of-ie^{-ix} ?
The first derivative of-ie^{-ix} is -cos(x)+isin(x)