
Differentiation and Implicit Functions
Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
Ethan Morris
FREE Resource
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the initial equation given in the problem?
2x + y^3 = 8
2xy^3 = 8
x^2 + y^3 = 8
2x^3y = 8
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which rule is applied to differentiate the product of two functions?
Power Rule
Product Rule
Chain Rule
Quotient Rule
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of y^3 with respect to t?
3y^2
3 dy/dt
3y^2 dy/dt
y^3 dy/dt
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the simplified form of the equation after applying the product rule?
2xy^3 dy/dt + 6y^2 dx/dt = 0
6xy^3 dy/dt + 2y^2 dx/dt = 0
6xy^2 dy/dt + 2y^3 dx/dt = 0
2xy^2 dy/dt + 6y^3 dx/dt = 0
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you isolate dx/dt in the equation?
Multiply both sides by 2y^3
Subtract 6xy^2 dy/dt from both sides
Divide both sides by 6xy^2
Add 6xy^2 dy/dt to both sides
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of y when x is substituted back into the original equation?
y = 4
y = cube root of 2
y = 1
y = 2
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What operation is used to find y from y^3 = 2?
Square both sides
Subtract 2 from both sides
Take the cube root of both sides
Multiply both sides by 3
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