082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

388 Chapter 11 Techniques of differentiation
df
= du
dt dt v +udv dt
Now wehave
du
= −0.1e −0.1t
dt
dv
=−sint
dt
So
df
= du
dt dt v +udv dt
df
= −0.1e −0.1t cost +e −0.1t (−sint)
dt
Rearranging gives
df
dt
= −e −0.1t (0.1cost +sint)
1
f(t)
0.8
0.6
0.4
0.2
–0.2
–0.4
–0.6
–0.8
–1
p 2p 3p 4p 5p 6p 7p 8p 9p 10p 11p 12p 13p 14p 15p
t
Figure11.1
Adamped sinusoidalsignal.
11.2.2 Thequotientrule
This rule allows us to differentiate a quotient of functions, such as
and e−3z
z 2 −1 .
x
sinx , t2 −t+3
t +2