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" 7."(1)/(sqrt(x+a))...

" 7."(1)/(sqrt(x+a))

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Differentiate from first principles: 7. (1)/( sqrt (x+1))

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The expression (1)/( sqrt( 3x +1)) [ ( ( 1+ sqrt( 3x + 1))/(2))^(7) - (( 1- sqrt ( 3x +1))/(2))^(7)] is a polynomial in x of degree eual to

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int_(0)^(7)(1)/(sqrt(4+3x))dx=

(7) int(1)/(sqrt(x+x sqrt(x)))dx