Derivatives of Natural Log, Exponentials, & Inverse Trig

Flashcard
•
Mathematics
•
11th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the derivative of the function y = 2^(3x + 4)?
Back
The derivative is y' = 3(ln(2))(2^(3x + 4)).
Tags
CCSS.HSF-IF.C.8B
2.
FLASHCARD QUESTION
Front
Find the derivative of y = 5x^2 e^(3x).
Back
The derivative is y' = 5xe^(3x)(3x + 2).
3.
FLASHCARD QUESTION
Front
What is the derivative of y = 3ln(x^2 - 3)?
Back
The derivative is y' = \frac{6x}{x^2 - 3}.
4.
FLASHCARD QUESTION
Front
What is the derivative of y = (3x^2 + 5)^(1/4)?
Back
The derivative is y' = \frac{3x}{2(3x^2 + 5)}.
5.
FLASHCARD QUESTION
Front
What is the chain rule in differentiation?
Back
The chain rule states that if a function y = f(g(x)), then the derivative y' = f'(g(x)) * g'(x).
6.
FLASHCARD QUESTION
Front
What is the product rule in differentiation?
Back
The product rule states that if u and v are functions of x, then the derivative of their product is (uv)' = u'v + uv'.
7.
FLASHCARD QUESTION
Front
What is the quotient rule in differentiation?
Back
The quotient rule states that if u and v are functions of x, then the derivative of their quotient is (u/v)' = (u'v - uv')/v^2.
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