Step 1: To differentiate an equation there is a simple rule to follow. For y=axⁿ dy/dx=anx^n-1. so for an example y=x³, dy/dx=3x^2. Therefore we just apply this rule into our equation.

Step 2: Break the equation down and do each factor of x seperately so 5x³ differentiates into 15x², -2x² differentiates to -4x, 7x differentiates to 7 and the 15 disappears from the end. This happens as the 15 just tells us where the line crosses the y axis and therefore has no bearing on the gradient.

Step 3: Put the differentiated parts back together to give the differentiated equation

dy/dx=15x²-4x+7