
2024 Derivative using Chain Rule& Higher Order (over 2 days)
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the Chain Rule in calculus?
Back
The Chain Rule is a formula for computing the derivative of the composition of two or more functions. It states that if you have two functions f(x) and g(x), then the derivative of their composition f(g(x)) is f'(g(x)) * g'(x).
2.
FLASHCARD QUESTION
Front
How do you find the derivative of a function raised to a power, such as f(x) = (g(x))^n?
Back
To find the derivative of a function raised to a power, use the Chain Rule: f'(x) = n * (g(x))^(n-1) * g'(x).
3.
FLASHCARD QUESTION
Front
What is the derivative of f(x) = (x^6 + 4)^5?
Back
f'(x) = 30x^5(x^6 + 4)^4, using the Chain Rule.
4.
FLASHCARD QUESTION
Front
How do you differentiate trigonometric functions like y = csc(u)?
Back
The derivative of y = csc(u) is y' = -csc(u)cot(u) * du/dx, where u is a function of x.
5.
FLASHCARD QUESTION
Front
What is the derivative of y = csc(8x^2)?
Back
dy/dx = -16xcsc(8x^2)cot(8x^2), applying the Chain Rule.
6.
FLASHCARD QUESTION
Front
What is the formula for the derivative of a polynomial function?
Back
The derivative of a polynomial function f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0 is f'(x) = n*a_n*x^(n-1) + (n-1)*a_(n-1)*x^(n-2) + ... + a_1.
7.
FLASHCARD QUESTION
Front
How do you find the derivative of a function like y = (2x + 1)^10?
Back
Use the Chain Rule: y' = 10(2x + 1)^9 * 2 = 20(2x + 1)^9.
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