

Derivatives the Chain Rule
Flashcard
•
Mathematics
•
11th - 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 a function y = f(g(x)), then the derivative y' is given by y' = f'(g(x)) * g'(x).
2.
FLASHCARD QUESTION
Front
How do you differentiate a function raised to a power, such as y = (u(x))^n?
Back
To differentiate a function raised to a power, use the power rule in conjunction with the Chain Rule: y' = n * (u(x))^(n-1) * u'(x), where u(x) is a function of x.
3.
FLASHCARD QUESTION
Front
What is the derivative of cos(x)?
Back
The derivative of cos(x) is -sin(x).
4.
FLASHCARD QUESTION
Front
How do you find the derivative of a composite function?
Back
To find the derivative of a composite function, apply the Chain Rule: differentiate the outer function and multiply it by the derivative of the inner function.
5.
FLASHCARD QUESTION
Front
What is the power rule for differentiation?
Back
The power rule states that if f(x) = x^n, then f'(x) = n * x^(n-1).
6.
FLASHCARD QUESTION
Front
What is the derivative of sin(x)?
Back
The derivative of sin(x) is cos(x).
7.
FLASHCARD QUESTION
Front
How do you differentiate a product of two functions, such as y = u(x)v(x)?
Back
To differentiate a product of two functions, use the product rule: y' = u'v + uv', where u and v are functions of x.
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