eDerivative

Example Find the derivative of the following function at the given point．

$\displaystyle f(z) = \frac{(z - i)}{(z + i)}, z = i$

Answer 1.

$\displaystyle f'(z)$	$\displaystyle =$	$\displaystyle \frac{(z-i)'(z+i)-(z-i)(z+i)'}{(z+i)^2}$
	$\displaystyle =$	$\displaystyle \frac{2i}{(z+i)^2}$

Thus，

$\displaystyle f'(i) = \frac{2i}{(i+i)^2} = \frac{2i}{-4} = -\frac{i}{2}$