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The following two examples show how you should aim to condense the solution. Example. Suppose we want to differentiate y2 + x3. − xy + cosy = 0 to find dy. Example 2: Find the equation of the tangent line that passes through point to the graph of. Solution: First we need to use implicit differentiation to find.The following problems require the use of implicit differentiation. Implicit differentiation is Click HERE to see a detailed solution to problem 1. We do not need to solve an equation for y in terms of x in order to find the derivative of y. Instead, we can use the method of implicit differentiation. This Example: x2 + y2 = r ; Subtract x2 from both sides:y2 = r2 − x ; Square root:y = ±√(r2 − x2) ; Let's do just the positive: y = √(r2 − x2) ; As a power: y = (r2 To find the implicit derivative,. Differentiate both sides of f(x, y) = 0 with respect to x; Apply usual derivative formulas to differentiate the x terms; Apply