The equation of circle ({eq}{x^2} + {y^2} = 25 {/eq}) is an example of an implicit function. The following formula helps us to find the derivative of an implicit function. {eq}\dfrac{d}{{dx}}y = \dfrac{d}{{dy}}y\left( {\dfrac{{dy}}...
Technically, you didn't differentiate equation 1 -- you took the differential of each side. If you differentate equation 1 with respect to x, you get (2) eixi = -sin(x) + icos(x) If you divide both sides by i, and do the usual trick of multiplying ##\frac{-\sin(x)}{i}##...