MA 123 CH 5

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Author:
clydethedog
ID:
25166
Filename:
MA 123 CH 5
Updated:
2010-06-29 22:12:33
Tags:
CALCULUS
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Description:
UK
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  1. Derivative of a constant function
    • if f(x) = c (a constant) then f '(x) = 0
    • the derivative of a constant is zero
  2. power rule
    • if f(x) = xn, then f '(x) = nxn-1
    • to take the derivative of x raised to a power, you multiply in front by the exponent and subtract 1 from the exponent
  3. constant multiple rule
    • let c be a constant and f(x) be a differentiable function
    • (cf(x))' = c(f '(x))
    • the derivative of a constant times a function equals the constant times the derivative of the function.
    • in other words, when computing derivatives, multiplicative constants can be pulled out of the expression
  4. sum rule
    • let f(x) and g(x) be differentiable functions
    • (f(x) + g(x))' = f '(x) + g'(x)
    • the derivative of a sum is the sum of the derivatives
  5. difference rule
    • let f(x) and g(x) be differentiable functions
    • (f(x) - g(x))' = f '(x) - g'(x)
    • the derivative of a difference is the difference of the derivatives
  6. product rule
    • let f (x) and g(x) be differentiable functions
    • (f(x)g(x))' = f '(x)g(x) + f(x)g'(x)
    • the derivative of a product equals the derivative of the first factor time the second one plus the first factor times the derivative of the second one
  7. quotient rule
    • (f '(x)g(x) - f(x)g'(x)) / (g(x))2
    • the derivative of a quotient equals the derivative of the top times the bottom minus the t0p times the derivatie of the bottom, all over the bottom squared

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