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Differentiate. x^(sqrtx)...

Differentiate.
`x^(sqrtx)`

Text Solution

Verified by Experts

`y=x^(sqrtx)`
In `y=sqrtxcdotInxrArr1/2dy/dx=1/(2sqrtx)Cdot In x+sqrtxcdot1/x`
`rArr dy/dx=x^(sqrtx){(Inx)/(2sqrtx)+1/sqrtx}=x^(sqrtx)(Inesqrtx)/sqrtx`
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