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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 ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Assignment ( section -A)
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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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  5. If t(1+x^(2))=x and x^(2)+t^(2)=y then at x = 2, the value of (dy)/(dx...

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  6. If x=tcost ,y=t+sint . Then (d^2 x)/(dy^2)at t=pi/2 is (a)(pi+4)/2...

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

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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)/(d...

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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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  17. The value of C ( if exists ) in Lagrange's theorem for the function |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. f(x)=sqrt(1-sqrt(1-x^2) then at x=0 ,value of f(x) is

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