Derivative_Formulas

Derivative_Formulas - Derivatives of specific functions [c]...

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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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This note was uploaded on 02/20/2009 for the course MATH 1300 taught by Professor Clark,br during the Spring '08 term at Colorado.

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