Differentiate 2x^3 - xy^2 - 4

Differentiate the first term 2x3 as normal by multiplying the coefficient of x by the power and subtracting the power by 1 to get 6x² . For the next term you have to use the product rule as you have two variables. Start by writing down the product of first variable ( x ) and the derivative of the second variable (2y dy/dx). Treat the y as if it were an x first BUT you must multiply the answer by dy/dx. Then add the second part of the product rule which is the product of derivative of the first variable (which is just 1) and the second variable (y² ). The second term is therefore 2xy(dy/dx)+ y² . The last term is simply 0 as in normal differentiation. The answer is 6x² - 2xy(dy/dx) +y² but it is best to write the answer in the form dy/dx = ( 6x² + y² )/ 2xy by rearranging.