Limits and Derivatives

Limits can exist even if the function is undefined at that point

A limit describes the behavior of a function near a point, which can exist independently of the function's actual value at that point.

Derivative of product = first function * second function's derivative + first function's derivative * second function

The product rule states that the derivative of a product of two functions is the first function times the derivative of the second, plus the derivative of the first function times the second function.

cos(x)

The derivative of sin(x) is cos(x), which is a fundamental result in trigonometric derivatives.

n * x^(n-1)

The power rule states that the derivative of x^n is n * x^(n-1), which works for any positive integer n.