We
havC
seen
many
ways
to
differentiate
combinations
of
polynomial
functions.
f(a)=
pla)tq(r)
then
=ptq'(r)
h'a)=f)
gla)+
f(r)
&'*)
h'()=
a))
sr)
Another
way
that
functions
are
often
combined
is
called
composition.
In
this
case,
one
function
1s
SUbSitutcd
Tor
another.
You
can
think
of
a
composite
function
as
an
input-output
diagram,
when
the
output
of
One
1unctOn
Is
used
as
the
input
for
a
second.
The
Derivatives
of
Composite
Functions
The
new
function,
f(g(x))
is
called
the
composition
function
of
f
and
g,
and
is
written
j
°8
input
(x)
function
g ’g)’function f
output
flgl)"
Sol:
a)
fo
glx)=
fg())=
Eg.I:
If
f(x)
=2
-3x
and
g(x)
= 5x*+x.
then
find
the
functions
f
ag
and
8oj
and
g°8.
c)
gogla)=
b)
g"f(x)=
gfu) =
he
chain
ralc
g(13r)
=
5(2-5
+2-3x)
S(5x+7)=
5(5xr'bxx)
Unit
2
-Activity
5
To
find
the
derivative
of
a
composite
funcion
hx)=
flg))
we
use
the
chain
rule.
denvatin
comosite
fup
hom
K)-{(g(a))has
a
eivahve
