Kalkulus Aturan Rantai Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

? y = (2x2 – 4x + 1)60 dy = dx Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

y = (2x2 – 4x + 1)60 u = 2x2 – 4x + 1 y = u60 dy du = 60u59 = 4x – 4 dx Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

y = (2x2 – 4x + 1)60 dy dx Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

y = (2x2 – 4x + 1)60 dy du du dx Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

y = (2x2 – 4x + 1)60 dy du = 60u59(4x–4) du dx Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

y = (2x2 – 4x + 1)60 dy du du dx = 60(2x2–4x+1)59(4x–4) Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

y = (2x2 – 4x + 1)60 dy dx = 60(2x2–4x+1)59(4x–4) Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

? x2(1 – x)3 y = 1 + x dy = dx Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

? y = sin [ cos (x2) ] dy = dx Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

Kalkulus Diferensial Lanjut Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

dy f'(x) Dxf(x) y' dx turunanpertama Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

d2y xf(x) f''(x) D2 y'' dx2 turunankedua Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

d3y xf(x) f'''(x) D3 y''' dx3 turunanketiga Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

d4y xf(x) f(4)(x) D4 y(4) dx4 turunankeempat Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

dny xf(x) f(n)(x) Dn y(n) dxn turunanke-n Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

? ? ? ? y = sin 2x d2y d3y = = dx2 dx3 d4y d12y d12y d12y = = dx4 dx12 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

Kalkulus Anti-diferensial Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

=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 http://wibiwardhono.lecture.ub.ac.id

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 http://wibiwardhono.lecture.ub.ac.id

=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 http://wibiwardhono.lecture.ub.ac.id

∫xr dx = xr+1 + C 1 r+1 Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

∫ sin x dx = -cos x + C Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

∫ cos x dx = sin x + C Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

∫[g(x)]r dx = [g(x)]r+1 + C Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id

∫(x2 + π)dx ∫(sin x – cos x) dx ∫(x3 + 6x)5 (6x2 + 12) dx Wibisono Sukmo Wardhono, ST, MT http://wibiwardhono.lecture.ub.ac.id