
Derivatives Using First Principles
Interactive Video
•
Mathematics
•
11th - 12th Grade
•
Hard
Thomas White
FREE Resource
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7 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main topic discussed in the video?
Applications of calculus
Derivatives using first principles
Limits and continuity
Integration techniques
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which function's derivative is being explored using the first principle?
sin(x)
cos(x)
e^x
ln(x)
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the definition of a derivative according to the video?
The limit as h approaches zero of (f(x+h) - f(x))/h
The limit of a function as x approaches infinity
The rate of change of a function
The integral of a function over a given interval
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in applying the first principle to find the derivative of e^x?
Simplify the expression
Apply the laws of exponents
Integrate the function
Use the definition of a derivative
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What transformation is introduced to simplify the limit expression?
Substituting n for e^h - 1
Using trigonometric identities
Applying integration by parts
Differentiating both sides
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the transformation imply about the behavior of n as h approaches zero?
n approaches infinity
n remains constant
n approaches zero
n becomes undefined
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the final result of the derivative of e^x using the first principle?
e^x
x^e
ln(x)
1/x
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