How does differentiation work?

Differentiation is essentially a method of finding the gradient of a function. To put that in better terms, imagine you have a graph of y=x, this is a straight line which means the gradient will always be the same. We can use the method of differentiation to find out what this gradient is. We use the formula: if y = x^n, then dy/dx = nx^(n-1). for this example since y = x^1. dy/dx = 1x^0, since any number to the power zero equals 1, dy/dx = 1. So our gradient is 1 which means that in our function, if we increase x by 1, y will also increase by 1.