Let f(z) = e^az . Use the limit : limz0zeaz1=a to show that f'(z) = ae^az .

Hint: Use ez1+z2=ez1z2 to show zf(z+z)f(z)=(zeaz1)eaz .

( so I am stucked at : eazlimz0zeaz1 . Do I set limz0zeaz1=a and say that it done?)