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If y=sqrt(x(log)e x) , then find (dy)/(d...

If `y=sqrt(x(log)_e x)` , then find `(dy)/(dx)` at `x=e` .

A

`(1)/(e)`

B

`(1)/(sqrt(e))`

C

`sqrt(e) `

D

`e^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given ,` y = sqrt(x log_(e) x )`
`rArr (dy)/(dx) = (1)/(2sqrt(x log_(e)) x)(d)/(dx) (x log_(e) x)`
= ` (1)/(2 sqrt( x log_(e) x))(x xx(1)/(x) + 1 log_(e)x)`
Now , ` ((dy)/(dx))_(x =e) = (1)/(2sqrt(2 xx 1)) (1 + 1) = (1)/(sqrt(e))` .
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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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  8. If y=cos(sinx^2) then at x=sqrt(pi/2), (dy)/(dx)=

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

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  13. If y = log (sin (x^(2))), 0 lt x lt (pi)/(2), "then " (dy)/(dx) "at ...

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  14. (d)/(dx)[log(e)e^(sin(x^(2)))] is equal to

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  15. If y=sqrt((1-x)/(1+x)), then (1-x^(2))(dy)/(dx)+y is equal to

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  16. Differential coefficient of sqrt(secsqrt (x)) is

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  17. (d)/(dx) [ log{e^(x) ((x-2)/(x +2))^(3//4)}] is equal to

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  18. Derivative of sqrte^(sqrt(x)) with respect to x is

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