PHYSIXMUS<br />4th<br />
2010. 3. 6 SAT<br />잘게 나누어 <br />관찰하기 2<br />1. 미분일반<br />
평균변화율<br />f(x2)-f(x1)<br />f(x)<br />x2-x1<br />f(x2)<br />f(x)<br />f(x)<br />x<br />f(x1)<br />평균속도<br />x<br />0<br />...
변화율Rate of change<br />f(x)<br />x2-x1->0<br />Q<br />f(x1)<br />f(x)<br />->?<br />x<br />P<br />F(x2)<br />F’(x1)<br />x...
기울기 Gradient<br />
도함수derivative<br />f’: x<br />f’(x)<br />
사례1 EXAMPLE1<br />f(x)=xn<br />f’(x)=nxn-1<br />
f(x+h)-f(x)<br />h->0<br />?<br />h<br />?<br />(x+h)n-xn<br />h->0<br />h<br />(nC0xn+n-1C0xn-1h+n-2C0xn-2h2+…+nCn-1xhn-1...
BB<br />BBB<br />BBBB<br />BBBBB<br />B<br />0<br />ABBBB<br />ABB<br />ABBB<br />A<br />AB<br />AABB<br />AABBB<br />AA<b...
사례2 EXAMPLE2<br />f(x)=sin x<br />f’(x)=cosx<br />
f(x+h)-f(x)<br />h->0<br />?<br />h<br />?<br />sin(x+h)-sinx<br />h->0<br />h<br />COMPUTER<br />cos x<br />
사례3 EXAMPLE3<br />f(x)=cos x<br />f’(x)=-sin x<br />
f(x+h)-f(x)<br />h->0<br />?<br />h<br />?<br />cos(x+h)-cosx<br />h->0<br />h<br />COMPUTER<br />-sin x<br />
사례4 EXAMPLE4<br />f(x)=tan x<br />f’(x)=sec2 x<br />
f(x+h)-f(x)<br />h->0<br />?<br />h<br />?<br />tan(x+h)-tanx<br />h->0<br />h<br />COMPUTER<br />sec2 x<br />
용어 Word<br />
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Physixmus 4th

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Physixmus 4th

  1. 1. PHYSIXMUS<br />4th<br />
  2. 2. 2010. 3. 6 SAT<br />잘게 나누어 <br />관찰하기 2<br />1. 미분일반<br />
  3. 3.
  4. 4. 평균변화율<br />f(x2)-f(x1)<br />f(x)<br />x2-x1<br />f(x2)<br />f(x)<br />f(x)<br />x<br />f(x1)<br />평균속도<br />x<br />0<br />X<br />x2<br />x1<br />
  5. 5. 변화율Rate of change<br />f(x)<br />x2-x1->0<br />Q<br />f(x1)<br />f(x)<br />->?<br />x<br />P<br />F(x2)<br />F’(x1)<br />x<br />x2<br />x1<br />
  6. 6. 기울기 Gradient<br />
  7. 7.
  8. 8. 도함수derivative<br />f’: x<br />f’(x)<br />
  9. 9. 사례1 EXAMPLE1<br />f(x)=xn<br />f’(x)=nxn-1<br />
  10. 10. f(x+h)-f(x)<br />h->0<br />?<br />h<br />?<br />(x+h)n-xn<br />h->0<br />h<br />(nC0xn+n-1C0xn-1h+n-2C0xn-2h2+…+nCn-1xhn-1+nCnhn)-xn<br />h<br />n-1C0xn-1+n-2C0xn-2h+…+nCn-1xhn-2+ nCnhn-1 <br />h->0<br />nxn-1<br />
  11. 11. BB<br />BBB<br />BBBB<br />BBBBB<br />B<br />0<br />ABBBB<br />ABB<br />ABBB<br />A<br />AB<br />AABB<br />AABBB<br />AA<br />AAB<br />AAABB<br />AAA<br />AAAB<br />AAAA<br />AAAAB<br />AAAAA<br />
  12. 12.
  13. 13. 사례2 EXAMPLE2<br />f(x)=sin x<br />f’(x)=cosx<br />
  14. 14. f(x+h)-f(x)<br />h->0<br />?<br />h<br />?<br />sin(x+h)-sinx<br />h->0<br />h<br />COMPUTER<br />cos x<br />
  15. 15. 사례3 EXAMPLE3<br />f(x)=cos x<br />f’(x)=-sin x<br />
  16. 16. f(x+h)-f(x)<br />h->0<br />?<br />h<br />?<br />cos(x+h)-cosx<br />h->0<br />h<br />COMPUTER<br />-sin x<br />
  17. 17. 사례4 EXAMPLE4<br />f(x)=tan x<br />f’(x)=sec2 x<br />
  18. 18. f(x+h)-f(x)<br />h->0<br />?<br />h<br />?<br />tan(x+h)-tanx<br />h->0<br />h<br />COMPUTER<br />sec2 x<br />
  19. 19.
  20. 20. 용어 Word<br />
  21. 21.
  22. 22. 2010. 3. 13 SAT<br />잘게 나누어 <br />관찰하기 3<br />1. 여러가지 미분 (Computer)<br />

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