Derivative-Solver.com
Derivatives
>
derivative of x^{e^x}
Derivatives
Multiple Derivatives
Partial Derivatives
Implicit Derivatives
Study Guides
d
dx
(
x
e
x
)
=
x
e
x
(
e
x
ln
(
x
)
+
e
x
x
)
Show Steps
« hide steps
d
dx
(
x
e
x
)
=
x
e
x
(
e
x
ln
(
x
)
+
e
x
x
)
steps
d
dx
(
x
e
x
)
Apply
exponent
rule
:
a
b
=
e
b
ln
(
a
)
x
e
x
=
e
e
x
ln
(
x
)
=
d
dx
(
e
e
x
ln
(
x
)
)
show steps
Apply
the
chain
rule
:
e
e
x
ln
(
x
)
d
dx
(
e
x
ln
(
x
)
)
=
e
e
x
ln
(
x
)
d
dx
(
e
x
ln
(
x
)
)
show steps
d
dx
(
e
x
ln
(
x
)
)
=
e
x
ln
(
x
)
+
e
x
x
=
e
e
x
ln
(
x
)
(
e
x
ln
(
x
)
+
e
x
x
)
show steps
e
e
x
ln
(
x
)
=
x
e
x
=
x
e
x
(
e
x
ln
(
x
)
+
e
x
x
)
Number Line