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Given y = sqrta^sqrt(x), "then" (dy)/(dx...

Given `y = sqrta^sqrt(x), "then" (dy)/(dx)` is equal to

A

`(y)/(2) ( sqrta^sqrt(x)log a)/(4y sqrt(x))`

B

`(y)/(2)`

C

` ( sqrta^sqrt(x)log a)/(4y sqrt(x))`

D

`s^(sqrt(x)) log a `

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Verified by Experts

The correct Answer is:
C
Given ` y sqrt(a^(sqrt(x)))`
` (dy)/(dx) = (1)/(2sqrt(a^(sqrt(x))) )xx(d)/(dx) (a^(sqrt(x)))`
` (1)/(2sqrt(a^(sqrt(x))) )xxa^(sqrt(x))log a (d)/(dx) (sqrt(x))`
`(a^(sqrt(x))loga)/(2sqrt(a^sqrt(x)))xx(1)/(2sqrt(x)) = (a^(sqrt(x))log a )/(4y sqrt(x))`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 2 (MISCELLANEOUS PROBLEMS)
  1. Given y = sqrta^sqrt(x), "then" (dy)/(dx) is equal to

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  2. If y = tan^(-1) (x)/(2) - cot ^(-1) (x)/(2) , "then" (dy)/(dx) is eq...

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  3. If y = ((x^(a))/(x^(b)))^(a + b) ((x^(b))/(x^(c)))^(b + c) ((x^(c))/(x...

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  4. If f(x) = 3^(x) " and" g(x) = 4^(x) , " then" (f'(0) - g'(0))/(1 +f'...

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  5. If y = sqrt((1+ sin x)/(1+ cos x)), " then" (dy)/(dx) is equal to

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  6. If y = tan^(-1) ((4sqrt(x))/(1 - 4x))" then" (dy)/(dx) is

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  7. If y = tan^(-1) ((4sqrt(x))/(1 - 4x))" then" (dy)/(dx) is

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  8. (d)/(dx) "" tan^(-1) ((2e^(x))/(1 - e^(2x)))=

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  9. If y = tan^(-1)((sin 3x - cos 3x )/(sin 3x + cos 3x))" then" (dy)/(dx...

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  10. If y = loga x + log xa + log x x + logaa, thendy/dx is equal to

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  11. If x = e^(x//y), then dy/dx is equal to

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  12. If f(x) = log ((m(x))/(n(x))), m(1) = n(1) = 1 and m'(1) = n'(1)...

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  13. If y = t^(2) + t - 1 " then " (dy)/(dx) is equal to

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  14. If xe^(xy)=y+sin^2x then at x=0 (dy)/dx=

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

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  16. Let y=e^(2x)dotT h e n((d^2y)/(dx^2))((d^2x)/(dy^2))i s

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  17. If f(x)=|x-2| and g(x)=f(f(x)), then g'(x)"for "x gt 20,is

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  18. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

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  19. The value of (d)/(dx) (|x-1| + |x -5|) at x = 3 is

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  20. If y=f(x)" and "ycosx+cosy=pi, then the value of f''(0) is

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