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37 Cards in this Set
- Front
- Back
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definition of the derivative |
F'(x) = lim as h approaches 0
[f(x+h) - f(x)] / h |
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derivative of a constant times a function
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d/dx (k(u(x))) = k du/dx
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Power Rule (variable raised to a constant)
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d/dx (u^n) = nu^(n-1) du/dx
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The Sum Rule
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d/dx (u+v) = du/dx + dv/dx
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The Difference Rule
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d/dx (u-v) = du/dx - dv/dx
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The Product Rule
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d/dx (uv) = uv' + vu'
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The Quotient Rule
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d/dx (u/v) = [vu' - uv'] / v^2
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The Chain Rule
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dy/dx = dy/du * du/dx
or d/dx (f(g(x)) = f'(g(x))g'(x) |
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The Derivative of the Sine
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d/dx (sinu) = cosu du/dx
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The Derivative of the Cosine
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d/dx (cosu) = -sinu du/dx
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The Derivative of the Tangent
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d/dx (tanu) = sec^2 u du/dx
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The Derivative of the Cotangent
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d/dx (cotu) = -csc^2 u
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The Derivative of the Secant
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d/dx (secu) = secu tanu du/dx
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The Derivative of the Cosecant |
d/dx (cscu) = -cscu cotu du/dx
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The Derivative of the Inverse Sine
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d/dx (Sin^-1 u) = 1/sqrt(1-u^2) du/dx
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The Derivative of the Inverse Cosine
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d/dx(Cos^-1 u) = -1/sqrt(1-u^2) du/dx
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The Derivative of the Inverse Tangent
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d/dx(Tan^-1 u) = 1/(1+u^2) du/dx
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The Derivative of the Inverse Cotangent
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d/dx(Cot^-1 u) = -1/(1+u^2) du/dx
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The Derivative of the Inverse Secant
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d/dx(Sec^-1 u) = 1/(|u|sqrt(u^2 - 1) du/dx
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The Derivative of the Inverse Cosecant
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d/dx(Csc^-1 u) = -1/(|u|sqrt(u^2 - 1) du/dx
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The Derivative of the Natural Log
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d/dx (ln u) = 1/u du/dx
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The Derivative of the log to base a
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d/dx (loga u) = 1/(u lna) du/dx
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The Derivative of e raised to a variable |
d/dx (e^u) = e^u du/dx
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The Derivative of a constant raised to a variable
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d/dx (a^u) = a^u lna du/dx
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Pythagorean Identities
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sin^2 x + cos^2 x = 1
tan^2 x +1 = sec^2 x 1 + cot^2 x = csc^2 x |
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sin even/odd formula
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sin (-x) = -sinx
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cos even/odd formula
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cos(-x) = cosx
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tan even/odd formula
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tan(-x) = -tanx
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csc even/odd formula
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csc(-x) = -cscx
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sec even/odd formula
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sec(-x) = secx
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cot even/odd formula
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cot(-x) = -cotx
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double angle formula: sin(2x)
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= 2sinx cosx
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double angle formula: cos(2x)
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= cos^2 x - sin^2 x
= 2cos^2 x - 1 = 1-2sin^2 x |
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half angle formula: cos^2 x
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= (1/2)(1+cos(2x))
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double angle formula: tan(2x)
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= (2tanx)/(1-tan^2 x)
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half angle formula: sin^2 x
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= (1/2)(1-cos(2x))
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half angle formula: tan^2 x
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= (1-cos(2x))/(1+cos(2x))
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