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If y = (lot (e) x)/(x) and z = log (e) x...

If `y = (lot _(e) x)/(x) and z = log _(e) x,` then ` (d ^(2) y)/(dz^(2)) + (dy)/(dz) =`

A

`e ^(-z)`

B

`2e ^(-z)`

C

`ze ^(-z)`

D

`-e^(-z)`

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The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIATION -EXERCISE 1D
  1. If x=a ( theta - sin theta), y =a (1 - cos theta) then y (2) at theta...

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  2. x = cos theta, y = sin 5 theta implies (1- x ^(2)) (d^(2)y)/(dx ^(2)) ...

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  3. If y = (lot (e) x)/(x) and z = log (e) x, then (d ^(2) y)/(dz^(2)) + ...

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  4. If x = Sin ^(-1) t, y = sqrt(1- t ^(2)) then (d^(2) y)/(dx ^(2))=

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  5. If y = ((1)/(x)) ^(x) then y (1) (1) =

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  6. If f (x ) = ((1)/(x)) ^(x) then f'' ((1)/(e)) =

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  7. (d ^(2) x)/(dy ^(2)) equals :

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  8. If y^2 = p(x) , a polyomial of degree 3 , then 2(d)/(dx)(y^3(d^2y)/(dx...

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  9. Let f (x) be a polynonial of degree 4 with f (2) =-1, f '(2) =0-, f ''...

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  10. Let f be a twice differentiable functin such that f''(x) - f(x) and f'...

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  11. If f:RrightarrowR is an even function having derivatives of all orders...

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  12. If f : RR to R is an even function which is twice differentiable on RR...

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  13. Let f(x) be a twice differentiable function and f^(11)(0)=2, then Lim(...

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  14. If P (x) is a polynomial of 2nd degree and P (2) =-1, P'(2) =0 and p''...

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  15. If P (x) is polynomial of 3rd degree and P''(1) =0, P'''(1)=6 then P '...

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  16. If f (x) = u//v then f '' (x) =

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  17. If f (x) = x^(n) then sum (r=0) ^(n) (f ^((r))(1))/(r 1) =

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  18. The nth derivative of log (ax+b) is

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  19. f (x) = sin x + cos x implies f ((pi)/(4)) f ^((iv)) ((pi)/(4)) =

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  20. The nth derivative of cos ^(4) x is

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