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Differentiate the following function with respect to x :

(xx) \(\sqrt{\text x}\)

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Let y =  (xx) \(\sqrt{\text x}\)

Taking log both the sides:

{Using product rule, \(\cfrac{d(uv)}{d\text x}=u\cfrac{dv}{d\text x}+v\cfrac{du}{d\text x}\)}

{\(\cfrac{d(log\,u)}{d\text x}=\cfrac{1}{u}\cfrac{du}{d\text x}\); Using chain rule,\(\cfrac{d(u+a)}{d\text x}=\cfrac{du}{d\text x}\) where a is any constant and u is any variable}

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