Differentiate x^3 + y^4 = 34 using implicit differentiation

An implicity function is one that is not expressed in the form y = f(x) such as the equation in the question. Instead of rearranging the equation to make y the subject, the equation can be differentiated using a technique called implicity differentiation. This involves differentiating each term on both sides of the equation. Differentiating x^3 will give 3x^2 and differentiating 34 will give 0. However differentiating y^4 will give (4y^3) X (dy/dx). This is achieved by using the chaing rule whereby d(y^4)/dx = (d(y^4)/dy) X (dy/dx).