Kalkulus Aturan Rantai Wibisono Sukmo Wardhono, ST, MT

Presentasi berjudul: "Kalkulus Aturan Rantai Wibisono Sukmo Wardhono, ST, MT"— Transcript presentasi:

1 Kalkulus Aturan Rantai Wibisono Sukmo Wardhono, ST, MT

2 ? y = (2x2 – 4x + 1)60 dy = dx Wibisono Sukmo Wardhono, ST, MT

3 y = (2x2 – 4x + 1)60 u = 2x2 – 4x + 1 y = u60 dy du = 60u59 = 4x – 4
dx Wibisono Sukmo Wardhono, ST, MT

4 y = (2x2 – 4x + 1)60 dy dx Wibisono Sukmo Wardhono, ST, MT

5 y = (2x2 – 4x + 1)60 dy du du dx Wibisono Sukmo Wardhono, ST, MT

6 y = (2x2 – 4x + 1)60 dy du = 60u59(4x–4) du dx
Wibisono Sukmo Wardhono, ST, MT

7 y = (2x2 – 4x + 1)60 dy du du dx = 60(2x2–4x+1)59(4x–4)
Wibisono Sukmo Wardhono, ST, MT

8 y = (2x2 – 4x + 1)60 dy dx = 60(2x2–4x+1)59(4x–4)
Wibisono Sukmo Wardhono, ST, MT

9 ? x2(1 – x)3 y = 1 + x dy = dx Wibisono Sukmo Wardhono, ST, MT

10 ? y = sin [ cos (x2) ] dy = dx Wibisono Sukmo Wardhono, ST, MT

11 Kalkulus Diferensial Lanjut Wibisono Sukmo Wardhono, ST, MT

12 dy f'(x) Dxf(x) y' dx turunanpertama Wibisono Sukmo Wardhono, ST, MT

13 d2y xf(x) f''(x) D2 y'' dx2 turunankedua
Wibisono Sukmo Wardhono, ST, MT

14 d3y xf(x) f'''(x) D3 y''' dx3 turunanketiga
Wibisono Sukmo Wardhono, ST, MT

15 d4y xf(x) f(4)(x) D4 y(4) dx4 turunankeempat
Wibisono Sukmo Wardhono, ST, MT

16 dny xf(x) f(n)(x) Dn y(n) dxn turunanke-n
Wibisono Sukmo Wardhono, ST, MT

17 ? ? ? ? y = sin 2x d2y d3y = = dx2 dx3 d4y d12y d12y d12y = = dx4 dx12
Wibisono Sukmo Wardhono, ST, MT

18 Wibisono Sukmo Wardhono, ST, MT

19 Kalkulus Anti-diferensial Wibisono Sukmo Wardhono, ST, MT

20 =2x f'(x) = ? g'(x) = ? h'(x) = ? g(x) = x2 + 3 f(x) = x2
h(x) = x2 – 2 3 =2x -2 Wibisono Sukmo Wardhono, ST, MT

21 g(x) antidiferensial f(x)
Jika Dxg(x) = f(x) Axf(x) = g(x) + C ∫f(x)dx = g(x) + C Wibisono Sukmo Wardhono, ST, MT

22 =2x ∫2x dx = x2 + C f'(x) = ? g'(x) = ? h'(x) = ? g(x) = x2 + 3
f(x) = x2 h'(x) = ? h(x) = x2 – 2 3 =2x ∫2x dx = x2 + C Wibisono Sukmo Wardhono, ST, MT

23 ∫xr dx = xr+1 + C 1 r+1 Wibisono Sukmo Wardhono, ST, MT

24 ∫ sin x dx = -cos x + C Wibisono Sukmo Wardhono, ST, MT

25 ∫ cos x dx = sin x + C Wibisono Sukmo Wardhono, ST, MT

26 ∫[g(x)]r dx = [g(x)]r+1 + C
Wibisono Sukmo Wardhono, ST, MT

27 ∫(x2 + π)dx ∫(sin x – cos x) dx ∫(x3 + 6x)5 (6x2 + 12) dx
Wibisono Sukmo Wardhono, ST, MT