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H2 Maths Notes
Differentiate
x
x
x^x
x
x
with logarithmic differentiation
Overview
Transcript
What you will learn
Set
y
=
x
x
y = x^x
y
=
x
x
and take natural logs so the exponent comes down.
Differentiate
ln
y
=
x
ln
x
\ln y = x \ln x
ln
y
=
x
ln
x
using chain rule on the left and product rule on the right.
Substitute
y
=
x
x
y = x^x
y
=
x
x
back in to get
x
x
(
ln
x
+
1
)
x^x(\ln x + 1)
x
x
(
ln
x
+
1
)
.
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