4/7 Derivative of Exponential and Logarithmic Functions

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Mathematics
•
12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the derivative of the function y=log_4(6x+5)?
Back
2.
FLASHCARD QUESTION
Front
Find the derivative of f(x) = xe^x.
Back
The derivative is f'(x) = e^x + xe^x.
3.
FLASHCARD QUESTION
Front
What is the slope of the tangent line for f(x)=\frac{e^{(x+1)}}{x+1} at x=-1?
Back
The slope is undefined.
4.
FLASHCARD QUESTION
Front
Find the derivative of f(x) = \frac{x^2}{e^x}.
Back
The derivative is f'(x) = \frac{(2x e^x - x^2 e^x)}{(e^x)^2}.
5.
FLASHCARD QUESTION
Front
What is the derivative of y=2^{3x+4}?
Back
The derivative is 3(\ln 2)(2^{3x+4}).
6.
FLASHCARD QUESTION
Front
Define the derivative of a function.
Back
The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point.
7.
FLASHCARD QUESTION
Front
What is the chain rule in differentiation?
Back
The chain rule states that if a function y is composed of two functions u and x, then the derivative is dy/dx = (dy/du)(du/dx).
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