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54 Cards in this Set
- Front
- Back
- 3rd side (hint)
d/dx (uv) |
u'v + v'u |
Product Rule |
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d/dx (u/v) |
(u'v - v'u) / v² |
Quotient Rule |
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f(g(x))' |
f'(g(x)) g'(x) |
Chain Rule |
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d/dx c |
0 |
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d/dx x |
1 |
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d/dx cx |
c |
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d/dx xⁿ |
nxⁿ ⁻ ¹ |
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d/dx eˣ |
eˣ |
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d/dx aˣ |
aˣ ln|a| |
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d/dx lnx |
1/x |
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d/dx logₐx |
1 / (x lna) |
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d/dx sinx |
cosx |
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d/dx cosx |
-sinx |
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d/dx tanx |
sec²x |
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d/dx cotx |
-csc²x |
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d/dx secx |
secx tanx |
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d/dx cscx |
-cscx cotx |
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d/dx arcsinx |
1 / √(1 - x²) |
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d/dx arccosx |
-1 / √(1 - x²) |
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d/dx arctanx |
1 / (1 + x²) |
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d/dx arccotx |
-1 / (1 + x²) |
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d/dx arcsecx |
1 / (|x| √(x² - 1)) |
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d/dx arccscx |
-1 / (|x| √(x² - 1)) |
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∫ dx |
x + C |
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∫ xⁿdx |
xⁿ ⁺ ¹ / (n + 1) + C (n ≠ - 1) |
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∫ dx/x |
lnx + C |
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∫ eˣ dx |
eˣ + C |
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∫ aˣ dx |
aˣ / (lna) + C |
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∫ lnx dx |
x (lnx - 1) + C |
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∫ sinx dx |
-cosx + C |
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∫ cosx dx |
sinx + C |
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∫ tanx dx |
-ln|cosx| + C |
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∫ cotx dx |
ln|sinx| + C |
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∫ secx dx |
ln|secx + tanx| + C |
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∫ cscx dx |
-ln|cscx + cotx| + C |
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∫ sec²x dx |
tanx + C |
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∫ csc²x dx |
-cotx + C |
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∫ secxtanx dx |
secx + C |
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∫ cscxcotx dx |
-cscx + C |
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∫ dx / √(a² - x²) |
arcsin(x / a) + C |
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∫ dx / (a² + x²) |
arctan(x / a) + C |
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∫ dx/(x √(x² - a²)) |
arcsec(|x| / a) + C |
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cscθ |
1 / sinθ |
Reciprocal Identity |
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secθ |
1 / cosθ |
Reciprocal Identity |
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cotθ |
1 / tanθ |
Reciprocal Identity |
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tanθ |
sinθ / cosθ |
Quotient Identity |
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cotθ |
cosθ / sinθ |
Quotient Identity |
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sin²θ + cos²θ |
1 |
Pythagorean Identity |
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tan²θ + 1 |
sec²θ |
Pythagorean Identity |
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1 + cot²θ |
csc²θ |
Pythagorean Identity |
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sin²(θ / 2) |
(1 - cosθ) / 2 |
Half-angle Formula |
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cos²(θ / 2) |
(1 + cosθ) / 2 |
Half-angle Formula |
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sin(2θ) |
2sinθcosθ |
Double-angle Formula |
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cos(2θ) |
cos²θ - sin²θ or 2cos²θ - 1 or 1 - 2sin²θ |
Double-angle Formula |