# Finding the derivative of g(x)

• Biosyn
In summary, the problem asked for the value of g'(0.1), which is equivalent to f'(0.3) multiplied by 3, using the chain rule. The given table provides the values of f'(x), so g'(0.1) can be calculated as 3*f'(0.3), which equals 3*1.096 = 3.288.
Biosyn

## Homework Statement

Let f(x) be a continuous and differentiable function on the interval 0 ≤ x ≤ 1, and let g(x)=f(3x). The table below gives values of f'(x), the derivative of f(x). What is the value of g'(0.1)?

http://img845.imageshack.us/img845/442/33806538.jpg

## The Attempt at a Solution

g(0.1) = f(3(0.1))
g(0.1) = f(0.3)
g'(0.1) = f'(0.3)
g'(0.1) = 1.096

Did I do the problem correctly? Thanks!

Last edited by a moderator:
Look correct assuming the picture and problems statement are what you have shown.

I think the answer should be E. g'(x) = 3*f'(3x). So, g'(0.1)=3*f'(0.3)=3*1.096=3.288

^ Actually that's correct because of the chain rule (haven't taken calculus in 5 years lol)

g(x) = f(u), where u = 3x so
g'(x) = f'(u)du = f'(3x)*3

shuohg said:
I think the answer should be E. g'(x) = 3*f'(3x). So, g'(0.1)=3*f'(0.3)=3*1.096=3.288

tazzzdo said:
^ Actually that's correct because of the chain rule (haven't taken calculus in 5 years lol)

g(x) = f(u), where u = 3x so
g'(x) = f'(u)du = f'(3x)*3

Thank you guys!
Forgot to use chain rule, thought I could just multiply 3*(0.3)

## 1. What is the definition of the derivative of a function?

The derivative of a function g(x) is the mathematical representation of the rate of change of the function at a specific point. It is defined as the slope of the tangent line to the graph of the function at that point.

## 2. How do you find the derivative of g(x) using the limit definition?

To find the derivative of g(x) using the limit definition, we can use the formula:
g'(x) = [g(x+h) - g(x)] / h
As h approaches 0, this formula gives us the slope of the tangent line to the graph of g(x) at x.

## 3. Can we find the derivative of any function?

Yes, the derivative of a function can be found for any differentiable function. A function is considered differentiable if its derivative exists at every point in its domain.

## 4. What is the relationship between the derivative and the original function?

The derivative of a function represents the instantaneous rate of change of the original function at a specific point. This means that the derivative and the original function are closely related and provide valuable information about each other.

## 5. How can we use the derivative of g(x) to analyze the behavior of the function?

The derivative of g(x) can provide information about the behavior of the function, such as the direction of the curve, the presence of extrema (maximum and minimum points), and the concavity of the graph. It can also be used to find the critical points and to solve optimization problems.

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