
Partial Derivatives and Differentiation Concepts

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

Mia Campbell
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 a function with respect to x?
Consider x as a constant and differentiate with respect to y.
Consider y as a constant and differentiate with respect to x.
Ignore the constants and differentiate directly.
Differentiate with respect to both x and y simultaneously.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When finding the partial derivative of f(x, y) = 2x^(-6)e^(3y) - x with respect to x, what is treated as a constant?
x
e^(3y)
2x^(-6)
Both x and y
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of differentiating x with respect to x?
1
x
0
x^2
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the partial derivative of f(x, y) = 2x^(-6)e^(3y) with respect to y, what rule is applied?
Power rule
Chain rule
Quotient rule
Product rule
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of e^(3y) with respect to y?
3e^(3y)
3
e^(3y)
0
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
For the function f(x, y) = 3x^(3.2)y^(7.6) + 32, what is the partial derivative with respect to x?
0
32
3x^(3.2)y^(7.6)
9.6x^(2.2)y^(7.6)
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When differentiating 3x^(3.2)y^(7.6) with respect to x, what is the exponent of x after differentiation?
7.6
2.2
1.2
3.2
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