How would you differentiate a function such as 4x^3

The general rule for differentiating functions such as 4x^3 is called the power rule.This formula goes by dy/dx of [x^n] = nx^(n-1)Now this may seem complicated but with examples hopefully it should become more clear!For instance, in the example you have used which is 4x^3. You would take 3 as the value of n (as that is the power) and input this into the formula. This would then produce 34x^(3-1) which simplifies to 12x^2.Another example would be to differentiate 6x^-2. The power can be any value so the formula works in the same way! There you take -2 as n which produces, -26x^(-2-1). This simplifies to -12x^-3 which is the answer!