
Partial Derivatives and Implicit Differentiation
Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
Lucas Foster
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in finding the partial derivative of z with respect to x using the implicit function theorem?
Solve for z
Set all terms to zero
Differentiate with respect to y
Move the constant to the other side of the equation
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When finding the partial derivative of z with respect to x, what is the derivative of x squared?
2x
x^2
0
x
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the implicit function theorem, what is the expression for f sub z?
3z^2
-3z^2
z^3
-z^3
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the alternative method introduced for finding partial derivatives?
Explicit differentiation
Implicit differentiation
Graphical differentiation
Numerical differentiation
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In implicit differentiation, what do you do when differentiating a z variable?
Subtract the partial derivative of z with respect to y
Ignore the z variable
Multiply by the derivative of x
Add the partial derivative of z with respect to x
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of differentiating y to the fourth with respect to y?
3y^2
0
y^4
4y^3
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the practice example, what is the partial derivative of z with respect to x?
2x^2z
3xy^2
y^3 + 2z^2
x^2 + y^3
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