
Understanding the Derivative of a^x

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

Sophia Harris
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the initial step in proving the derivative of a^x?
Using the power rule
Using integration by parts
Setting up a logarithmic equation
Applying the product rule
Tags
CCSS.HSF.BF.B.5
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the equivalent logarithmic equation for a^x = y?
log base x of a = y
log base a of y = x
log base y of a = x
log base a of x = y
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is implicit differentiation used in this proof?
To avoid using the chain rule
To handle the term containing y
To directly find the derivative
To simplify the equation
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the derivative of log base a of y with respect to x expressed?
x times dx/dy
1 over y times dy/dx
1 over x times dx/dy
y times dy/dx
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What mathematical rule is applied due to the presence of y in the equation?
Product rule
Quotient rule
Chain rule
Power rule
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of the change of base formula in this proof?
To find the integral of the function
To eliminate the need for implicit differentiation
To convert the base to 10
To simplify the differentiation process
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the role of the natural log in the change of base formula?
It is used to find the integral
It is irrelevant to the proof
It serves as a constant
It acts as a variable
Tags
CCSS.HSF-IF.C.8B
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