can anyone explain me a clearer, easy way to find the derivative of a function of a graph.?

Question

I know you find the slope but what do we use the slope for. I believe there has to be an easier way than finding the slope? Does anyone know? I very confused about this topic. Plz help> Thnx

Answer 1

The formal approach for finding the derivative is very easy once you get used to it--far easier then calculating the anti-derivative.

Answer 2

Well, the derivative is the slope. If you find the derivative of a given function, then you pop out another function that represents the slope of the graph. For example, say you have a function y = f(x) (a function depending only on x). The deriviative can be written f'(x) or y', or even dy/dx which means you are taking a function y, and differentiating by the variable x. If you plug a value for x into the derivative, then you will get the slope of the point with the given x value on the original function of the graph (called instantanious slope). With some practice, finding derivatives is easy (you can do it without looking at the graph) and very necessary. They hold important applications involving rate of change (also known as slope of a graph) and can be applied to most any subject form economics to the underlying workings of a computer.

Answer 3

The simplest way of taking a derivative is as follows. It's easiest to show by example: Suppose you have the following formula for a parabola: f(x)= x^2+2x+1. In this case, you differentiate by parts. The way you do this is to take the value of the exponent for each term, and multiply it by the coefficient of the variable. You then subtract 1 from the value of the exponent. Note thta the constant term - in this case the 1 - becomes a 0 after differentiation. So, in my example, you get:

f'(x)=2x^1 + (2)(1)x^0 + 0 or written more clearly:

f'(x)=2x+2

in general terms: if y=cx^n, then dy/dx=cnx^n-1

Note, however, that as you move through calculus, it is essential that you understand the "slope" version of differentiation, and why the simple method above matches the "slope" method. If you don't you'll get lost really quickly as things get more complicated.

Also, please note that this is only the simplest form of differentiation. As equations become harder, you'll learn about the chain rule and the like.

Answer 4

Unfortunately, the derivative is all about the slope of the function. It may help to think of it as "rate of change" instead. This will take you back to the definition of a derivative as change in y / change in x. The change in "y" is the rise or elevation change of the slope. The change in "x" is the "run" or horizontal change of the slope.