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If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,...

If `u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e n(d u)/(d v)` is `3/2xcosx^3cos e cx^2` `2/3sinx^3secx^2` `tanx` (d) none of these

A

`3/2 x cos x^(3) cosec x^(2)`

B

`2/3 "" sin x^(3) sec x^(2)`

C

` tan x `

D

`3/2 x sin x^(2) sec x^(3)`

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The correct Answer is:
A
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AAKASH INSTITUTE-CONTINUITY AND DIFFERENTIABILITY-Assignment ( section -A)
  1. If y = sin x^(@) " and " u = cos x " then " (dy)/(dx) is equal to

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  2. Let the function y = f(x) be given by x= t^(5) -5t^(3) -20t +7 ...

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  3. If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...

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  4. The differential coefficient of sec^(-1)(1/(2x^2-1)) w.r.t sqrt(1-x^2)...

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  5. If t(1+x^2)=x and x^2+t^2=y then dy/dx at x=2 is

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  6. x=t cost, y=t+sin t. Then (d^2 x)/(dy^2) at t=pi/2 is

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  7. if y = sin 2x , " then " (d^(6)y)/(dx^(6)) " at" x = pi/2 is equal to

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  8. Let f(x) =|{:(x^(3), sinx,cosx),(6,-1,0),(p,p^(2),p^(3)):}| where p is...

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  9. If x=2a t , y=a t^2 , where a is a constant, then find (d^2y)/(dx^2...

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  10. If y = x^(1/x) , the value of (dy)/(dx) at x =e is equal to

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  11. If y = tan^(1-) sqrt((x+1)/(x-1)) " for " |x| gt 1 " then " (dy)/(dx)...

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

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  13. if f'(x)=sqrt(2x^2-1) and y=f(x^2) then (dy)/(dx) at x=1 is:

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  14. Let the function f(x) be defined as f(x) = {:{((logx-1)/(x-e) , xnee),...

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  15. Rolle's theorem is not applicable to f(x) = |x| in [ -2,2] because

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  16. Lagrange's mean value theorem is not applicable to f(x) in [1,4] where...

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  17. The value of c in Lagrange's mean value theorem for the function f(x) ...

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  18. If f be a function such that f(9)=9 and f'(9)=3, then lim(xto9)(sqrt(f...

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  19. If f(x) = {{:(1/(1+e^(1//x)), x ne 0),(0,x=0):} then f(x) is

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  20. If f(x)=sqrt(1-sqrt(1-x^2) then at x=0

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