Differentiate the equation y^2 + y = x^3 + 2x

To answer this question you must use implicit differentiation due to there being both x and y terms. Consequently you must differentiate each term individually as you would usually (by multiplying by the power and taking one off the power) but for the y terms due to chain rule the differentiated term must also be multiplied by dy/dx. Consequently the answer becomes: 2y*dy/dx + dy/dx = 3x^2 + 2. The equation must then be rearranged to make dy/dx the subject dy/dx (2y + 1) = 3x^2 + 2 Therefore dy/dx = (3x^2 + 2)/(2y+1)