differentiate the function of ax^2n+bx^n+c
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Answer:
Remember that the derivative of a sum is the sum of the derivatives.
(
y
(
x
)
+
g
(
x
)
+
z
(
x
)
)
'
=
y
'
(
x
)
+
g
'
(
x
)
+
z
'
(
x
)
In this case
f
(
x
)
=
y
(
x
)
+
g
(
x
)
+
z
(
x
)
where
y
(
x
)
=
a
x
2
g
(
x
)
=
b
x
and
z
(
x
)
=
c
First remember the derivative of a constant is zero
Therefore
z
(
x
)
=
c
⇒
z
'
(
x
)
=
0
By the fact that
(
c
f
(
x
)
)
'
=
c
f
'
(
x
)
)
and by the power rule
(
x
n
)
'
=
n
x
n
−
1
g
(
x
)
=
b
x
=
b
x
1
⇒
g
'
(
x
)
=
(
b
x
1
)
'
=
b
(
x
1
)
'
=
b
(
1
x
1
−
1
)
=
b
x
0
=
b
(
1
)
=
b
and
y
(
x
)
=
a
x
2
⇒
y
'
(
x
)
=
(
a
x
2
)
'
=
a
(
x
2
)
'
=
2
a
x
2
−
1
=
2
a
x
1
=
2
a
x
Then we plug in
f
'
(
x
)
=
y
'
(
x
)
+
g
'
(
x
)
+
z
'
(
x
)
=
2
a
x
+
b
+
0
=
2
a
x
+
b
−−−−−−−
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