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derivative of x^{sqrt(x)}
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d
dx
(
x
√
x
)
=
x
√
x
(
ln
(
x
)
2
√
x
+
1
√
x
)
Show Steps
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d
dx
(
x
√
x
)
=
x
√
x
(
ln
(
x
)
2
√
x
+
1
√
x
)
steps
d
dx
(
x
√
x
)
Apply
exponent
rule
:
a
b
=
e
b
ln
(
a
)
x
√
x
=
e
√
x
ln
(
x
)
=
d
dx
(
e
√
x
ln
(
x
)
)
show steps
Apply
the
chain
rule
:
e
√
x
ln
(
x
)
d
dx
(
√
x
ln
(
x
)
)
=
e
√
x
ln
(
x
)
d
dx
(
√
x
ln
(
x
)
)
show steps
d
dx
(
√
x
ln
(
x
)
)
=
ln
(
x
)
2
√
x
+
1
√
x
=
e
√
x
ln
(
x
)
(
ln
(
x
)
2
√
x
+
1
√
x
)
show steps
e
√
x
ln
(
x
)
=
x
√
x
=
x
√
x
(
ln
(
x
)
2
√
x
+
1
√
x
)
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