Calculate dy/dx if ln (x + y) = ex/y

answer:     ======use implicit differentiation: differentiate both sides with respect to x.    focusing on the left-hand side, use the chain rule.the outside "function" is ln(x) and the inside "function" is x+ythe derivative of outside function, ln(x) is 1/x. stick the inside function into the derivative of outside to get 1/(x+y).then multiply by derivative of inside.    focusing on the right-hand side, use the quotient rule."low d high minus high d low; draw a line and square below."    joining these two together in the original equation:     multiply both sides by  to cancel out the  in the denominator.    multiply both sides by  to cancel out the  in the denominator.then start expanding. we need to solve for dy/dx.    move all terms with  together; move everything else to the other side.    factor out dy/dx from left-side, then divide both sides by that large thing to isolate dy/dx.