
Differentiation and Gradient Concepts
Interactive Video
•
Mathematics
•
11th - 12th Grade
•
Practice Problem
•
Hard
Aiden Montgomery
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main challenge of using the Cartesian approach to find the tangent to an ellipse?
Complexity of the ellipse equation
Absence of parametric forms
Lack of a clear point of interest
Inability to use implicit differentiation
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is implicit differentiation useful in this context?
It simplifies the equation of the ellipse
It allows differentiation without isolating y
It provides a direct solution for x
It eliminates the need for Cartesian coordinates
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of a constant with respect to x?
The constant itself
Zero
The constant times x
One
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When applying the chain rule, what is the first step?
Add the derivatives of both functions
Differentiate the outside function
Multiply by the derivative of the outside function
Differentiate the inside function
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of differentiating x^2 with respect to x?
2x^2
x
x^2
2x
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why might y appear in the derivative when using implicit differentiation?
Because y is eliminated during differentiation
Because y is not a function of x
Because x and y are entangled in the equation
Because y is a constant
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the expected sign of the gradient in the first quadrant?
Undefined
Zero
Negative
Positive
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