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if y = log(​​sqrtx+1/sqrtx) prove that dy/dx = x-1/2x(x+1)

if y = log(​​sqrtx+1/sqrtx) prove that dy/dx = x-1/2x(x+1)

Grade:12

1 Answers

Govardhan T C
13 Points
5 years ago
solution:j
       dy /dx = 1/ ( \sqrt x + 1/ \sqrt x ) * ( 1/ 2\sqrt x - 1/ 2\sqrt (x^3{}) = \sqrt x / (1+x) * 1/ 2\sqrt x ( 1 - 1/\sqrt (x^2{}) ) = 1/ (1+x) * 1/2(1-1/x) = 1/ (1+x) * 1/2( x-1 / x ) = (x-1) / 2x (1+x))

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