Question

Finding the derivative using the definition method, what is the derivative of the function?

A) 0
B) 1
C) 2
D) tan(2x)

Answer 1

The derivative of a function using the definition method involves taking the limit as the difference in x approaches 0.

Step-by-step explanation:

The derivative of a function using the definition method involves taking the limit as the difference in x approaches 0. Let's use an example to illustrate this. Suppose we have the function f(x) = x^2. To find the derivative using the definition method, we can start by evaluating the difference quotient:

lim (h -> 0) [f(x + h) - f(x)] / h

Plugging in the expression for f(x), we get:

lim (h -> 0) [(x + h)^2 - x^2] / h

Expanding and simplifying, we have:

lim (h -> 0) [2hx + h^2] / h

Canceling out the h term, we are left with:

lim (h -> 0) 2x + h

Since the limit as h approaches 0 is simply 0, our derivative is:

2x