MA 123 CH 5

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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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 Author: clydethedog ID: 25166 Filename: MA 123 CH 5 Updated: 2010-06-30 02:12:33 Tags: CALCULUS Folders: Description: UK Show Answers:

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