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If y =sqrt(x) + (1)/(sqrt(x)) , "then" ...

If ` y =sqrt(x) + (1)/(sqrt(x)) , "then" 2 x . (dy)/(dx) ` is equal to

A

` sqrt(x) + (1)/(sqrt(x))`

B

`(1)/(2sqrt(x)) - 2 sqrt(x)`

C

`sqrt(x) - (1)/(sqrt(x))`

D

`(x +1)/(sqrt(x))`

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `y = sqrt(x) + (1)/(sqrt(x))`
On differentiating both sides w.r.t.x, we get
`(dy)/(dx) = (1)/(2sqrt(x)) - (1)/(2(x)^(3//2))`
` = (1)/(2) ((1)/(sqrt(x)) -(1)/(x sqrt(x))) = ((x-1))/(2xsqrt(x))`
`rArr (2xdy)/(dx) = sqrt(x) - (1)/(sqrt(x))`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 1 DERIVATIVE OF COMPOSITE FUNCTION (BY CHAIN RULE )
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  11. If y=cos(sinx^2) then at x=sqrt(pi/2), (dy)/(dx)=

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  12. Derivative of log[log(log x^(5))] with respect to x is

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  13. If f(x) = log(x^(2)) (log(e) x) "then f' (x) at x= e" is

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  14. If y = log(2) log(2) (x) , " then " (dy)/(dx) is equal to

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  15. If x=(1-sqrt(y))/(1+sqrt(y)) then (dy)/(dx) is equal to

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