What is the basic formula for the derivative of an inverse function?

Understanding Derivatives of Inverse Functions

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard

Ethan Morris
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The derivative of the inverse function is the negative of the original function's derivative.
The derivative of the inverse function is one over the derivative of the original function.
The derivative of the inverse function is the square of the original function's derivative.
The derivative of the inverse function is the same as the original function.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of inverse functions, what does switching x and y help achieve?
It helps find the original function
It helps find the derivative of the original function
It helps find the slope of the tangent line
It helps find the inverse function
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example y = x^2 - 7, what is the derivative of the inverse function in terms of y?
2x
2y
1 / (2y)
1 / (2x + 7)
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which method involves switching x and y and using implicit differentiation?
Direct differentiation
Implicit differentiation
Algebraic manipulation
Graphical analysis
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in finding the derivative of an inverse function using implicit differentiation?
Differentiate both sides with respect to y
Switch x and y
Solve for y
Find the inverse function
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the third method for finding the derivative of the inverse function?
Directly differentiating the inverse function
Using the original function's derivative
Using a graphical approach
Applying the chain rule
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example y = x^2 + 2x + 1, what is the derivative of the inverse function in terms of x?
1 / (2x + 1)
2√x
2x + 1
1 / (2√x)
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