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Algebra
Math
| Term | Definition |
|---|---|
| (a+b)^2 | a^2+2ab+b^2 |
| (a-b)^2 | a^2-2ab+b^2 |
| a^2-b^2 | (a+b)(a-b) |
| a^3+b^3 | (a+b)(a^2-ab+b^2) |
| a^3-b^3 | (a-b)(a^2+ab+b^2) |
| (a+b)^3 | a^3+3a^2b+3ab^2+b^3 |
| (a-b)^3 | a^3-3a^2b+3ab^2-b^3 |
| a[n] | a[n-1]+d; a[1]+(n-1)*d |
| S ар | (а[1]+a[n])*n / 2 |
| b[n] | b[n-1]*q; b[1]*q^(n-1) |
| S гео | (q^n - 1)*b[1] / q-1 |
| a[0] | 1 |
| a^-1 | 1/a |
| a^0.5 | v(a) |
| a^m * a^n | a^(m+n) |
| (ab)^n | a^n + b^n |
| (a^m)^n | a^(m*n) |
| a^1 | 1 |
| a^-n | 1 / a^n |
| a^(1/n) | nv(a) |
| a^m / a^n | a^(m-n) |
| (a/b)^n | a^n / b^n |
| a^(m/n) | nv(a^m) |
| loga(1) | 0 |
| loga(a) | 1 |
| loga(bc) | loga(b)+loga(c) |
| loga(b/c) | loga(b)-loga(c) |
| loga(b^n) | n*loga(b) |
| loga^m(b) | 1/m * loga(b) |
| loga(b) | 1 / logb(a) |
| loga(b) | logc(b) / logc(a) |
| a^logc(b) | b^logc(a) |
| a^loga(b) | b |
| cos(2x) разные | cos(x)^2 - sin(x)^2 |
| cos(2x) cos | 2cos(x)^2 - 1 |
| cos(2x) sin | 1 - 2sin(x)^2 |
| sin(2x) | 2sin(x)*cos(x) |
| tg(2x) | 2tg(x) / 1-tg(x)^2 |
| sin(x+y) | sin(x)*cos(y) + sin(y)*cos(x) |
| sin(x-y) | sin(x)*cos(y) - sin(y)*cos(x) |
| cos(x+y) | cos(x)*cos(y) - sin(x)*sin(y) |
| cos(x-y) | cos(x)*cos(y) + sin(x)*sin(y) |
| tg(x+y) | tg(x)+tg(y) / 1 - tg(x)*tg(y) |
| tg(x-y) | tg(x)-tg(y) / 1 + tg(x)*tg(y) |
| sin(x) + sin(y) | 2*sin((x+y)/2)*cos((x-y)/2) |
| sin(x) - sin(y) | 2*sin((x-y)/2)*cos((x+y)/2) |
| cos(x) + cos(y) | 2*cos((x+y)/2)*cos((x-y)/2) |
| cos(x) - cos(y) | -2*sin((x+y)/2)*sin((x-y)/2) |
| sin(0.5x) | V(1-cos(x) / 2) |
| cos(0.5x) | V(1+cos(y) / 2) |
| tg(0.5x) | sin(x) / 1+cos(x) |
| (u*v)‘ | u‘v + uv‘ |
| (u/v)‘ | u‘v-uv‘ / v^2 |
| (x^n)‘ | n*x^(n-1) |
| (v(x))‘ | 1 / 2*v(x) |
| (1/x)‘ | - 1/x^2 |
| (e^x)‘ | e^x |
| (ln(x))’ | 1/x |
| (a^x)’ | a^x * ln(a) |
| (loga(x))’ | 1 / x*ln(a) |
| (sin(x))’ | cos(x) |
| (cos(x))’ | -sin(x) |
| (tg(x))’ | 1 / cos(x)^2 |
| (ctg(x))’ | - 1 / sin(x)^2 |
Created by:
Q--3
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