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dy<br />
dx = dy du<br />
= (−csch u)(b) = −b csch (a + bt)<br />
du dx<br />
Jika y = f(x) = sech x , maka dy = f'(x) = −tanhx sechx (5.53)<br />
dx<br />
Bukti<br />
y = f(x) = sechx = 1<br />
coshx<br />
Misal u = 1 v = coshx<br />
du<br />
dy<br />
dx = dx<br />
du<br />
dx = 0<br />
dv<br />
dx = sinhx<br />
dv<br />
. v − u.<br />
dx (0)(coshx) − (1)(sinhx)<br />
= = −sinhx = −tanhx sechx (terbukti)<br />
v<br />
cosh x<br />
cosh x<br />
Jika y = sech u dan u = f(x) , maka dy<br />
du<br />
= −tanhu sechu<br />
dx dx<br />
(5.54)<br />
Bukti<br />
y = sech u ® dy = −tanhu sechu<br />
du<br />
dy<br />
dx = dy du<br />
du<br />
= −tanhu sechu<br />
du dx dx (terbukti)<br />
Contoh 5.29<br />
Jika y = 2 sech( 1 3 − 1 dy<br />
x), tentukan<br />
5 dt<br />
Penyelesaian<br />
Misal u = 1 3 − 1 5 x<br />
y = 2 sechu<br />
du<br />
dx = − 1 dy<br />
= −2 tanhu sechu<br />
5<br />
du<br />
dy<br />
dx = dy du<br />
du dx = (−2 tanhu sechu)(− 1 5 ) = 2 tanhu sechu<br />
5<br />
= 2 5 tanh 1 3 − 1 5 x sech 1 3 − 1 5 x<br />
Jika y = f(x) = csch x , maka dy = f'(x) = −cschx cothx (5.55)<br />
dx<br />
Bukti<br />
y = f(x) = cschx = 1<br />
sinhx<br />
Misal u = 1 v = sinhx<br />
du<br />
dx = 0<br />
dv<br />
dx = coshx<br />
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