A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It tells us how much a function is changing at a given point and in what direction.
To find the derivative of a function, you can use the formula: f'(x) = lim(h→0) [f(x+h) - f(x)]/h. This formula is known as the definition of a derivative and can be used to find the derivative at any point of a given function.
The derivative of a function is important because it helps us understand the behavior of the function. It can tell us if the function is increasing or decreasing at a given point, and it can also help us find the maximum and minimum points of a function.
When we say "find the derivative at 1", we are referring to finding the derivative of a function at the point x = 1. This means we are interested in knowing the rate of change of the function at the specific point x = 1.
To find the derivative at 1 of a complicated function, we can use the same formula as mentioned in question 2, but we need to substitute x = 1 in the formula. If the function is too complicated, we can also use other methods such as the chain rule, product rule, or quotient rule to find the derivative at 1.