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Derivative_Formulas

Derivative_Formulas - Derivatives of specific...

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IB 10/08/08 General derivative formulas, applying to arbitrary functions f(x) and g(x) [cf(x)]´ = c [f´(x)] Multiplicative constant rule [f(x)+g(x)]´ = f´(x) + g´ x) Sum rule [f(x)-g(x)]´ = f´ x) - g´(x) Difference rule [f(x)g(x)]´ = f(x)g´(x) + g(x)f´(x) Product rule [f(x)/g(x)]´ = (g(x)f´(x) – f(x)g´(x)) / (g(x)) 2 Quotient rule dy/dx = (dy/du) (du/dx) Chain rule (Leibniz) [f(g(x))]´ = f´(g(x)) g´(x) Chain rule (Newton) (Derivative of the outside function evaluated at the inside function, times the derivative of the inside function)
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Unformatted text preview: Derivatives of specific functions [c]´ = 0 Derivative of a constant [x r ]´ = rx r-1 Power rule (r is any real constant) Trig functions: [sin x]´ = cos x [cos x]´ = – sin x [tan x]´ = sec 2 x [cot x]´ = – csc 2 x [sec x]´ = sec x tan x [csc x]´ = – csc x cot x Logarithm functions: [ln x]´ = 1/x x > 0 [ln |x|]´ = 1/x x ≠ 0 [log b x]´ = 1 / (x (ln b)) x > 0, b constant: b > 0, b ≠ 1 [log b |x|]´ = 1 / (x (ln b)) x ≠ 0, b constant: b > 0, b ≠ 1 Exponential functions: [e x ]´ = e x [b x ]´ = b x (ln b) b constant, b > 0 Inverse trig functions: [sin-1 x]´ = 1 / √ 1 – x 2 [cos-1 x]´ = –1 / √ 1 – x 2 -1 <= x <= 1 [tan-1 x]´ = 1 / (1 + x 2 )...
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