# Using logarithmic differentiation or otherwise, differentiate x^(x^2)?

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I calculated this and got the right answer according to Symbolab. My solution was #(x^(x^2))(x+2xlnx)# However, the solution for #y=x^(x^2)# on the worksheet I've been provided is #dy/dx = (x^((x^2)+1))(2lnx+1)#

How have they managed to get this?

I calculated this and got the right answer according to Symbolab. My solution was

How have they managed to get this?

##### 1 Answer

Apr 24, 2018

check the explanation below

#### Explanation:

**Taking the natural logarithm of both sides**

**Differentiate**

**Multiply by #y#**

Take **common factor**