How do you differentiate y=x^x?

Reid Berger

Reid Berger

Answered question

2023-03-19

How to differentiate y = x x ?

Answer & Explanation

moventseexi

moventseexi

Beginner2023-03-20Added 5 answers

Logarithmic differentiation can be used.
Take the natural logarithm of both sides
ln y = ln x x
Then, using properties of logarithms, rewrite the right hand side
ln y = x ln x
Differentiate both sides with respect to x.
Use the product rule on the right side
1 y d y d x = ln x + x 1 x
1 y d y d x = ln x + 1
Multiply both sides by y
d y d x = y ( ln x + 1 )
Next, y = x x . Thus, we can write
d y d x = x x ( ln x + 1 )

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