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Popular >

derivative of e^{i2x}

Solution

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

Solution

- 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

Popular Examples

derivative of f(-5)=sqrt(x)+6 derivative of

f (- 5) = x + 6

integral of 1/(s+1)

\int \frac{1}{s + 1} d s

(\partial)/(\partial x)(x^{-1}+ln(z^2))

\frac{\partial}{\partial x} (x^{- 1} + ln (z^{2}))

simplify (x^2)/6-x simplify

\frac{x ^{2}}{6} - x

sum from n=1 to infinity of 5(2/3)^{n-1}

n = 1 \sum \infty 5 (\frac{2}{3})^{n - 1}

Frequently Asked Questions (FAQ)

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