How do you differentiate #f(x)=x^(x^2)#?

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Sep 14, 2016

Let # y = x^(x^2)#

Taking log on both sides,

#logy=logx^(x^2)#

By logarithmic properties,

#logy=x^2*logx#

Differentiating the equation using chain rule and product rule,

#1/ydy/dx=2x*logx+x^2/x#

#dy/dx=x^(x^2)(2xlogx+x )= x^(x^2+1)*(logx^2+1)#

If you have any kind of confusion or want me to elaborate in the steps of solving, comment below.

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