Solve for the Derivative of Inverse Function g

In summary, the derivative of an inverse function is the slope of the tangent line at a given point on the inverse function's graph, representing the rate of change of the original function. To find the derivative of an inverse function, you can use the formula g'(x) = 1/f'(g(x)), where f'(x) is the derivative of the original function. The derivative of a function and its inverse are reciprocals of each other, meaning that if the derivative of f(x) is g'(x), then the derivative of g(x) is 1/g'(x). The derivative of an inverse function can be negative if the original function is decreasing at a certain point. Finding the derivative of an inverse function is important
  • #1
intenzxboi
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Homework Statement


Suppose that f has an inverse and f (6) = 18, f'(6) = 4/5. If g = 1/(f-1), what is g'(18)?

have no idea how to set up problem
 
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  • #2
Do you read your textbook at all? If not then you should! In it you'll find a theorem that specifically deals with derivatives of inverse functions. Please flip through the section in which this exercise occurs and see if you can't find it. Then we can get started.
 

1. What is the derivative of an inverse function?

The derivative of an inverse function is the slope of the tangent line at a given point on the inverse function's graph. It represents the rate of change of the original function at that point.

2. How do you find the derivative of an inverse function?

To find the derivative of an inverse function g, you can use the formula:
g'(x) = 1 / f'(g(x)), where f'(x) is the derivative of the original function f(x).

3. What is the relationship between the derivative of a function and its inverse?

The derivative of a function and its inverse are reciprocals of each other. This means that if the derivative of f(x) is g'(x), then the derivative of g(x) is 1/g'(x).

4. Can the derivative of an inverse function be negative?

Yes, the derivative of an inverse function can be negative. This can happen when the original function is decreasing at a certain point, resulting in a negative slope for the inverse function at that point.

5. Why is finding the derivative of an inverse function important?

Finding the derivative of an inverse function is important because it allows us to calculate the rate of change of the original function at a specific point. This is useful in many real-life applications, such as optimization problems and physics calculations.

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