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Popular >

derivative of e^{xi}

Solution

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

Solution

- sin (x) + i cos (x)

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

(\partial)/(\partial x)(8/(x^2+y^2+z^2))

\frac{\partial}{\partial x} (\frac{8}{x ^{2} + y ^{2} + z ^{2}})

sum from n=1 to infinity of (4/3)^n

n = 1 \sum \infty (\frac{4}{3})^{n}

integral of 3cos^2(x)sin(x)

\int 3 cos^{2} (x) sin (x) d x

integral of (2t^2+3)^{4/3}t^3

\int (2 t^{2} + 3)^{\frac{4}{3}} t^{3} d t

derivative of f(x)=(x^2+3x-1)e^x derivative of

f (x) = (x^{2} + 3 x - 1) e^{x}

Frequently Asked Questions (FAQ)

What is the derivative of e^{xi} ?
The derivative of e^{xi} is -sin(x)+icos(x)
What is the first derivative of e^{xi} ?
The first derivative of e^{xi} is -sin(x)+icos(x)