# What is the derivative of y= (e^(ix)-e^(-ix) )/2?

##### 1 Answer
Mar 21, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = i \left(\frac{{e}^{i x} - {e}^{- i x}}{2}\right)$

#### Explanation:

Use the chain rule:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{{e}^{i x} \left(i\right) - {e}^{- i x} \left(- i\right)}{2}$

$= \frac{i {e}^{i x} + i {e}^{- i x}}{2}$

Alternatively

Point out that $y = i \sin x$, so $\frac{\mathrm{dy}}{\mathrm{dx}} = i \cos x$