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Let f be a function defined for all `x in R`. If f is differentiable and `f(x^(3)) = x^(5)` for all `x in R (x ne 0)`, then the value of `f^(')(27)` is

A

15

B

45

C

0

D

10

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A
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HIMALAYA PUBLICATION-DIFFERENTIATION-QUESTION BANK
  1. If y = f(x) is an odd function, which is differentiable, defined on (-...

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  2. Let f(x) be a polynomial function such that f(x). f(1/x) = f(x) + f(1/...

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  3. Let f be a function defined for all x in R. If f is differentiable and...

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  4. If f(x ) = (ax +b) sin x + (cx +d) cosx, then the values of a,b,c,d su...

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  5. If x = a(t+1/t), y =a(t-1/t), then dy/dx =

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  6. f(x) = log (x+ sqrt(x^(2)+1), then f^(')(1/2) =

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  7. If f '(x) = cos (log x) and y = f((2x-3)/(2x+5)) then dy/dx =

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  8. If 2^(x)+2^(y)=2^(x+y), then (dy)/(dx) is

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  9. If y = (x^(x))^(x), then (dy/dx)(x =1) =

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  10. If y = tan^(-1) (cosec x - cot x), then dy/dx =

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  11. If y = (e^(x)+1)/(e^(x)-1), then y^(2)/2 + dy/dx =

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  12. y = (x+ sqrt(x^(2)+a^(2)))^(n), then dy/dx =

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  13. If y = 1 + x + x^(2)/(2!) + x^(3)/(3!)+x^(4)/(4!)+ ....., then dy/dx =

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  14. The least value of n so that y(n) = y(n+1), where, y = x^(2)+e^(x) is

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  15. If y = (1+ 1/x)^(x), then dy/dx =

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  16. If y =(sin x)^(tan x), then dy/dx =

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  17. A differentiable function f(x) is such that f91) =7 and f^(')(1) = 1/7...

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  18. The differentiable coefficient of x^(6) w.r.t. x^(3) is :

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  19. (d)/(dx)((x)/(2)sqrt(x^(2)+a^(2))+(a^(2))/(2)log(x+sqrt(x^(2)+a^(2))))...

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  20. If y = f((2x-1)/(x^(2)+1)) and f^(')(x) = sin x^(2), then dy/dx =

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