What is the first step in finding the derivative of x raised to the x using logarithmic differentiation?

Derivatives of Exponential and Logarithmic Functions

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Mathematics
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9th - 12th Grade
•
Hard

Ethan Morris
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Apply the power rule
Use the product rule
Use logarithmic differentiation
Differentiate directly
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the formula for the derivative of u raised to the v, what does 'v u prime' represent?
The quotient of v and u
The product of v and the derivative of u
The derivative of v with respect to u
The sum of v and u
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When finding the derivative of x raised to the sin x, what is the derivative of sin x?
1
x
sin x
cos x
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the simplified form of the derivative of ln x raised to the x?
x times ln x
x raised to ln x times ln x
ln x raised to x times 1/ln x plus ln ln x
ln x times x
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the derivative of x raised to ln x, what is the expression for v prime?
1
x
ln x
1/x
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the final simplified form of the derivative of x raised to ln x?
x raised to ln x times ln x
x raised to ln x times 2 ln x over x
ln x times x
x times ln x
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of e^x with respect to x?
e^x
1
x
ln x
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