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Calculus 2, Unit 1
Integrals, derivatives, tables, etc.
| Term | Definition |
|---|---|
| Derivative of any constant | 0 |
| Derivative of x | 1 |
| Derivative of x^n | nx^(n-1) |
| Derivative of e^x | e^x |
| Derivative of n^x | (n^x)(lnx) |
| Derivative of sinx | cosx |
| Derivative of cosx | -sinx |
| Derivative of tanx | sec^2x |
| Derivative of cotx | -csc^2x |
| Derivative of secx | secxtanx |
| Derivative of cscx | -cscxcotx |
| Derivative of arcsinx, or the inverse of sinx | 1/√(1-x^2) |
| Derivative of arccosx, or the inverse of cosx | -1/√(1-x^2) |
| Derivative of arctanx, or the inverse of tanx | 1/(1+x^2) |
| Derivative of arccotx, or the inverse of cotx | -1/(1+x^2) |
| Derivative of arcsecx, or the inverse of secx | 1/(x√(x^2-1)) |
| Derivative of arccscx, or the inverse of cscx | -1/(x√(x^2-1)) |
| Integral of 0dx | C |
| Integral of 1dx | x + C |
| Integral of x^ndx | x^n+1/n+1 + C |
| Integral of e^xdx | e^x |
| Integral of 1/xdx | lnx + C |
| Integral of n^x | n^x/lnx |
| Integral of cosxdx | sinx + C |
| Integral of sinxdx | -cosx + C |
| Integral of sec^2xdx | tanx + C |
| Integral of csc^2xdx | -cotx + C |
| Integral of tanxsecxdx | secx + C |
| Integral of cotxcscxdx | -cscx + C |
| Integral of 1/√1-x^2dx | arcsinx + C |
| Integral of -1/√1-x^2dx | arccotx + C |
| Integral of 1/x√x^2-1dx | arcsecx + C |
| Integral of -1/x√x^2-1dx | arccscx + C |
| Double Angle Formula of sin2Θ | 2sinΘcosΘ |
| Double Angle Formula of cos2Θ | cos^2Θ-sin^2Θ = 2cos^2Θ-1 = 1 - 2sin^2Θ |
| Double Angle Formula of tan2Θ | 2tanΘ/1 - tanΘ |
| Half Angle Formula of sin^2Θ | 1-cos2Θ/2 |
| Half Angle Formula of sinΘ/2 | +-√1-cosΘ/2 |
| Half Angle Formula of cos^2Θ | (1+cos2Θ)/2 |
| Half Angle Formula of cosΘ/2 | +-√1+cosΘ/2 |
| Half Angle Formula of tanΘ/2 | +-√1-cosΘ/1+cosΘ or sinx/1+cosx or 1-cosx/sinx |
| Substitution for √a^2-x^2 | x = asinΘ |
| Derivative Substitution for √a^2-x^2 | dx = a cosΘdΘ |
| Trig Identity for √a^2-x^2 | cos^2Θ = 1 - sin^2Θ |
| Result for √a^2-x^2 | acosΘ |
| Substitution for √a^2+x^2 | x = atanΘ |
| Derivative Substitution for √a^2+x^2 | dx = asec^2ΘdΘ |
| Trig Identity for √a^2+x^2 | 1 + tan^2Θ = sec^2Θ |
| Result for √a^2+x^2 | asecΘ |
| Substitution for √x^2-a^2 | x = a secΘ |
| Derivative substitution for √x^2-a^2 | dx = asecΘtanΘdΘ |
| Trig Identity for √x^2-a^2 | tan^2Θ = sec^2Θ-1 |
| Result for √x^2-a^2 | atanΘ |
| logb(M * N) | logbM + logbN |
| logbM + logbN | logb(M*N) |
| logb(M/N) | logbM-logbN |
| logbM-logbN | logb(M/N) |
| logb(M^k) | klogbM |
| klogbM | logb(M^k) |
| logb(1) | 0 |
| logb(b) | 1 |
| logb(b^k) | k |
| b^logb(k) | k |
| ∫udv | uv - ∫vdu |
| sin(Θ) on a triangle | o/h |
| cos(Θ) on a triangle | a/h |
| tan(Θ) on a triangle | o/a |
| csc(Θ) | h/0 |
| sec(Θ) | h/a |
| cot(Θ) | a/o |
| Reciprocal Identity for sinΘ | 1/cscΘ |
| Reciprocal Identity for cosΘ | 1/secΘ |
| Reciprocal Identity for tanΘ | 1/cotΘ |
| Reciprocal Identity for cscΘ | 1/sinΘ |
| Reciprocal Identity for secΘ | 1/cosΘ |
| Reciprocal Identity for cotΘ | 1/tanΘ |
| Pythagorean Trig Identity 1a | sin^2Θ + cos^2Θ = 1 |
| Pythagorean Trig Identity 1b | cos^2Θ = 1 - sin^2 |
| Pythagorean Trig Identity 1c | sin^2Θ = 1 - cos^2Θ |
| Pythagorean Trig Identity 2a | 1 + tan^2Θ = sec^2Θ |
| Pythagorean Trig Identity 2b | tan^2Θ = sec^2Θ - 1 |
| Pythagorean Trig Identity 2c | 1 = sec^2Θ - tan^2Θ |
| Pythagorean Trig Identity 3a | 1 + cot^2Θ = csc^2Θ |
| Pythagorean Trig Identity 3b | cot^2Θ = csc^2Θ - 1 |
| Pythagorean Trig Identity 3c | 1 = csc^2Θ - cot^2Θ |
| Inverse sin(arcsin) | Θ = sin^-1(o/h) |
| Inverse cosine (arccos) | Θ = cos^-1(a/h) |
| Inverse tangent (arctan) | Θ = tan^-1(o/a) |
| (x^a) * (x ^b) | x^a+b |
| x^a+b | (x^a) * (x^b) |
| (x^a)/(x^b) | x^a-b |
| x^a-b | (x^a)/(x^b) |
| (x^a)^b | x^ab |
| x^ab | (x^a)^b |
| (xy)^a | (x^a)(y^a) |
| (x^a)(y^a) | (xy)^a |
| (x/y)^a | (x^a)/(y^a) |
| x^-a | 1/x^a |
| x^0 | 1 |
| ln(e) | 1 |
Created by:
mozomari
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