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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
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power rule
- if f(x) = xn, then f '(x) = nxn-1to take the derivative of x raised to a power, you multiply in front by the exponent and subtract 1 from the exponent
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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
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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
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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
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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
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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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