If y=sin x cos xe^x, then find
dy/dx
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Answer:
differentiate using the
product rule
Given
y
=
g
(
x
)
.
h
(
x
)
then
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
d
y
d
x
=
g
(
x
)
h
'
(
x
)
+
h
(
x
)
g
'
(
x
)
2
2
∣
∣
∣
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
here
g
(
x
)
=
e
x
⇒
g
'
(
x
)
=
e
x
and
h
(
x
)
=
sin
x
+
cos
x
⇒
g
'
(
x
)
=
cos
x
−
sin
x
⇒
d
y
d
x
=
e
x
(
cos
x
−
sin
x
)
+
e
x
(
sin
x
+
cos
x
)
×
×
x
=
e
x
cos
x
−
e
x
sin
x
e
x
sin
x
+
e
x
cos
x
×
×
x
=
2
e
x
cos
x
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