Calculus I: Limits & Derivatives
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What does a limit describe?
The value a function approaches as the input approaches some point.
What is a derivative?
The instantaneous rate of change of a function, the slope of its tangent line.
What is the power rule for derivatives?
The derivative of x^n is n times x^(n-1).
What is the derivative of a constant?
Zero.
What is the derivative of sin(x)?
cos(x).
What is the derivative of e^x?
e^x itself.
What does the product rule state?
d/dx[f g] = f'g + f g'.
What does the chain rule state?
The derivative of a composite f(g(x)) is f'(g(x)) times g'(x).
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