If
y
=
x
2
e
x
y=x^2e^x
y
=
x
2
e
x
, then
y
′
=
y'=
y
′
=
2
x
e
x
2xe^x
2
x
e
x
2
x
+
e
x
2x+e^x
2
x
+
e
x
x
(
x
+
2
e
x
)
x(x+2e^x)
x
(
x
+
2
e
x
)
x
e
x
(
x
+
2
)
xe^x(x+2)
x
e
x
(
x
+
2
)
Summary
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Approach
Apply the product rule.
y
=
x
2
e
x
y=x^2e^x
y
=
x
2
e
x
y
′
=
x
2
(
e
x
)
′
+
e
x
(
x
2
)
′
y'=x^2(e^x)'+e^x(x^2)'
y
′
=
x
2
(
e
x
)
′
+
e
x
(
x
2
)
′
=
x
2
e
x
+
e
x
(
2
x
)
= x^2e^x+e^x(2x)
=
x
2
e
x
+
e
x
(
2
x
)
=
x
e
x
(
x
+
2
)
= \boxed{xe^x(x+2)}
=
x
e
x
(
x
+
2
)