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AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Monday, December 05, 2005

Blogging on Related Rates

Instead of reflecting, I'm going to list some information that might help you understand differentiating functions.

Constant Function f (x) = c f'(x) = 0
Constant Multiple Rule d/dx [c*f(x)] = c*f'(x)
Sum and Difference Rule d/dx[f(x) + g(x)] = f'(x) + g'(x) you can replace the + signs with a - sign
Power Rule d/dx(x^n) = nx^(n-1)
Derivative of e^x d/dx(e^x) = e^x
Exponential Function d/dx(a^x) = (ln a)*a^x
Product Rule d/dx[f (x)*g (x)] = f (x)*g'(x) + f'(x)*g (x)
Quotient Rule d/dx [f(x)/g(x)] = [g(x)*f'(x) - f(x)*g'(x)]/[g(x)]^2
Derivatives of Trigonometric Functions
d/dx (sin x) = cos x
d/dx (cos x) = -sin x
d/dx (tan x) = sec^2 x
d/dx (csc x) = -csc x cot x
d/dx (sec x) = sec x tan x
d/dx (cot x) = -csc^2 x
The Chain Rule [fog]' (x) = f'(g(x))*g'(x)
d/dx (ln x) = 1/x
Local linearization of f at x = a f (x) ~ f(a) + f'(a)(x-a)

All of these derivative rules are probably going to be on the test, so it is a good idea to learn how to use them. I excluded related rates because that depends on the question, and there is no definite formula for all related rates problems. These formulas and derivatives cover most of the unit and they are good to know.



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