How do you differentiate #e^(x / y) = 8x - y#?
Since we cannot obtain y as an explicit function of x, we will use the method of implicit differentiation to find the derivative of y with respect to x.
In so doing, we must bear in mind that y is a function of x.
We rearrange the expression and then take the derivative on both sides using normal rules of differentiation to obtain
Note we used the quotient rule in the last term since y is a function of x so x/y represents a quotient of 2 functions in x.
Rearranging we get