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)

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

- 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)

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

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

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

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

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

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)