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Derivative of sqrte^(sqrt(x)) with re...

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

A

` (sqrte^(sqrt(x)))/(2sqrt(xe)^sqrt(x))`

B

` (4e^(sqrt(x)))/(sqrt(xe)^sqrt(x))`

C

` (e^(sqrt(x)))/(4sqrt(xe)^sqrt(x))`

D

` (e^(sqrt(x)))/(sqrt(e)^sqrt(x))`

Text Solution

Verified by Experts

The correct Answer is:
C
Let ` y = (e^(sqrt(x)))^(1//2)`
On differentiating both sides of Eq .(i) w.r.t.x, we get
` (dy)/(dx) = (1)/(2) (e^(sqrt(x)))^((1)/(2)1) (d)/(dx) e^(sqrt(x))`
` rArr (dy)/(dx) = (e^(sqrt(x)))/(2sqrt( e^(sqrt(x))))(d)/(dx) (sqrt(x)) = (1)/(2)(e^(sqrt(x)))/(sqrt(esqrt(x)))xx(1)/(2sqrt(x))`
`rArr = (e^(sqrtx))/(4sqrt(x)sqrt(e^(sqrt(x))))=(e^(sqrt(x)))/(4sqrt(xe^(sqrtx)))` .
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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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  2. Derivative of sqrt( tan sqrt(x)) with respect to x is

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  3. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is

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  4. If y = sqrt(sin + y ) "then" (dy)/(dx) is equal to

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  5. The differential coefficient of sin (cos (x^(2))) with respect to s i...

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

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  7. If y= ( cos x ^(2))^(2) , "then" (dy)/(dx) is equal to

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  8. If y=cos(sinx^2) then at x=sqrt(pi/2), (dy)/(dx)=

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

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

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

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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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  19. The derivative of y = sec^(-1) ((1)/(8x)) is

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  20. If y = sin^(-1) (cos x) , then derivative of y is

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