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Contoh 5.8<br />
Jika y = sin(p − 2x), tentukan dy<br />
dx<br />
Penyelesaian<br />
Misa u = –2x y = sin u<br />
du<br />
dx = −2<br />
dy<br />
dx = dy du<br />
du dx<br />
dy<br />
du = cos u<br />
= (cos u)(−2) = −2cos(p − 2x)<br />
Contoh 5.9<br />
Jika y = cos x dy<br />
, tentukan<br />
2 dx<br />
Penyelesaian<br />
Misal u = x y = cos u<br />
2<br />
du<br />
dx = dy du<br />
du dx = (−sin u)(1 2 ) = − 1 2 sin x 2<br />
Contoh 5.10<br />
Jika y = sin2x cos 3x, tentukan dy<br />
dx<br />
Penyelesaian<br />
Misa u = sin2x v=cos3x<br />
du<br />
dx = 2cos2x dv<br />
dx = −3sin3x<br />
dy<br />
dx = du<br />
dx . v + u dv = (2cos2x)(cos3x) + (sin2x)(−3sin3x)<br />
dx<br />
= 2cos2x cos3x − 3sin2x sin3x)<br />
Contoh 5.11<br />
Jika y = sin3x<br />
cos4x<br />
Penyelesaian<br />
Misal u = sin 3x<br />
du<br />
dx = 3cos3x<br />
, tentukan<br />
dy<br />
dx<br />
du dv<br />
dy<br />
dx = . v − u.<br />
dx dx<br />
v<br />
=<br />
v = cos 4x<br />
dv<br />
dx = −4sin4x<br />
(3cos3x)(cos4x) − (sin3x)(−4sin4x)<br />
=<br />
(cos4x)<br />
3cos3x cos4x + 4sin3x sin4x)<br />
cos 4x<br />
Jika y = f(x) = tan x , maka dy = f'(x) = sec x (5.17)<br />
dx<br />
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