# Find Derivative of 3/x+2 using f(x+h) - (fx) / h

• pooker
In summary, the conversation is about finding derivatives the long way and the question of whether or not to plug in a given value after finding the derivative. The teacher expects the value to be plugged into the definition of the derivative at a given point, and the correct substitution for this specific example would be x=8 instead of x=2.
pooker
Our teacher wants us to find derivatives the long way

f(x+h) - (fx) / h

So anyways, on one of my questions 3 / x + 2 , x=8

I know how to find the derivative of 3 / x+2 , but why was their an x=8 next to it? Am I supposed to plug this in after finding the derivative?

yes, you need to plug it in for x after you find the derivative.

I disagree with mathstudent88. The basic definition of 'derivative' is 'derivative at a given point'. From what you say, I imagine your teacher is expecting you to put it directly into the definition of the derivative of f at x0:
$$\lim_{h\rightarrow 0} \frac{f(x_0+ h)- f(x_0)}{h}$$
which, for f(x)= 3/(x+2), at x0= 8 is
$$\lim_{h\rightarrow 0}\frac{3/((8+h)+2)- 3/(8+2)}{h}$$
$$= \lim_{h\rightarrow 0}\frac{3/(10+h)- 3/10}{h}$$

Last edited by a moderator:
With the obvious substitution of x=8 instead of x=2

Thanks, OfficeShredder, I've edited that mistake. (So, now I can pretend I never made it!)

## 1. What is the purpose of finding the derivative of 3/x+2 using f(x+h) - (fx) / h?

The purpose of finding the derivative of a function is to determine the rate of change of that function at a specific point. In this case, we are using the formula f(x+h) - (fx) / h to find the derivative of the function 3/x+2.

## 2. How do you use the formula f(x+h) - (fx) / h to find the derivative of a function?

To use this formula, you need to substitute the value of x+h and fx into the formula. Then, you need to simplify the equation and take the limit as h approaches 0. This will give you the derivative of the function at a specific point.

## 3. Can you provide an example of using the formula f(x+h) - (fx) / h to find the derivative of a function?

Sure, let's say we have the function f(x) = 3x+4. To find the derivative at a specific point, let's say x = 2, we will use the formula f(x+h) - (fx) / h. So, f(x+h) = 3(x+h)+4 and fx = 3x+4. Substituting these values into the formula, we get (3(x+h)+4 - (3x+4)) / h. Simplifying this equation and taking the limit as h approaches 0, we get the derivative of the function at x = 2, which is 3.

## 4. What is the importance of finding the derivative of a function?

The derivative of a function is important because it gives us information about the rate of change of that function at a specific point. This information is useful in many real-world applications, such as calculating velocity, acceleration, and optimization problems.

## 5. Is there an easier way to find the derivative of a function?

Yes, there are other methods for finding the derivative of a function, such as using the power rule, product rule, quotient rule, and chain rule. These methods are often easier to use than the formula f(x+h) - (fx) / h, especially for more complex functions. It is important to learn and understand these different methods for finding derivatives to be able to choose the most efficient one for a given function.

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