<s>[INST] Differentiate $x^{x^2}$ with respect to $x^2$ I am doing it by $x^2$  as the and differentiating both of the above separately and then deciding them
I got answer $x^{x^2} (2\log x+1))/2$
I don't know if it is correct 
 [/INST] $$\frac{dx^{x^2}}{dx^2}=\frac{de^{x^2\log x}}{2x\,dx}=\frac{2x\log x+x}{2x}x^{x^2}=\frac{2\log x+1}2x^{x^2}.$$

Alternatively,
$$\frac{d\sqrt{x^2}^{x^2}}{dx^2}=\frac{de^{{x^2\log x^2/2}}}{dx^2}=\frac{\log x^2+1}2e^{{x^2\log x^2/2}}=\frac{2\log x+1}2x^{x^2}.$$
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