MA 123 CH 5
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Derivative of a constant function
 if f(x) = c (a constant) then f '(x) = 0
 the derivative of a constant is zero

power rule
 if f(x) = x^{n}, then f '(x) = nx^{n1}
 to take the derivative of x raised to a power, you multiply in front by the exponent and subtract 1 from the exponent

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

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

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

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

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