Differentiate the following equation: y = 2(x^3) - 6x

Firstly we look at the term 2(x^3). The power of x (in this case 3) is multiplied by the factor of x (in this case 2) and the power is then reduced by 1. This means it is 2x3(x^{3-1}) which simplifies to 6(x^2) This process is repeated for the second term in the sequence which is -6x. The power of x is 1 so when multipled by -6 it stays as -6. The power of x is reduced by 1 which makes it x^0. Anything to the power of 0 is 1 so the term -6x becomes -6. Below is the working out written mathematically: y = 2(x^3) -6x dy/dx = 6(x^2) - 6 dy/dx = 6(x^2 -1)