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If y = (1 + (2)/(x)) (1 + (2)/(x))(1 + (...

If `y = (1 + (2)/(x)) (1 + (2)/(x))(1 + (3)/(x))...(1 + (n)/(x))`
` x ne 0 , "then " (dy)/(dx) ` when x = - 1 is

A

nl

B

`(n-1)l`

C

`(-1)^n(n-1)l`

D

`(-1)^n nl`

Text Solution

Verified by Experts

The correct Answer is:
C
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TARGET PUBLICATION-DIFFERENTIATION -EVALUATION TEST
  1. If y=f((3x+pi)/(5x+4)) and f'(x)=tan^2 x, then (dy)/(dx) at x=0 is

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  2. If y=|cosx|+|sinx|, then (dy)/(dx)" at "x=(2pi)/(3) is

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  3. If y = (1 + (2)/(x)) (1 + (2)/(x))(1 + (3)/(x))...(1 + (n)/(x)) x ...

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  4. If f(x)=x/(1+|x|) for x in R, then f'(0) =

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  5. If y=f((2x+3)/(3-2x)) and f(x)=sin(logx), then (dy)/(dx)=

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  6. d/(dx)[atan^(-1)x+blog((x-1)/(x+1))]=1/(x^4-1)=>a-2b=

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  7. If f(x) = cos x cos 2x cos 4x cos (8x). cos 16x then find f' (pi/4)

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  8. If d/(dx)((1+x^4+x^8)/(1+x^2+x^4))=ax^3+bx,then

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  9. If 2x=y^(1/5)+y^(-1/5) then (x^2-1)(d^2y)/dx^2+xdy/dx=ky , then find t...

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  10. if sqrt(x^2+y^2)=ae^(tan^-1 (y/x)) , a > 0, (y(0) > 0) then y"(0) equa...

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  11. If f(x), g(x), h(x) are polynomials in x of degree 2 If F(x)=|[f,g,h],...

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  12. If y= cos ax and yn is n^(th) derivative of y, then |{:(y,y1,y2),(y3...

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  13. If y = sin[cos^(-1){sin(cos^(-1) x)}], "then" (dy)/(dx)" at x" = (1)/...

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  14. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

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  15. If the function f defined on R-{0} os a dIfferentiable function and f(...

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  16. If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x), then the value ...

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  17. If y=f(x^3),z=g(x^5),f'(x)=tanx and g'(x)=sec x, then (dy)/(dz)=

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  18. If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3),p rov et h a t(dy)/(dx)=(x^2)/(y...

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  19. Let fx) be a polynomial function of second degree. If f(1)= f(-1) and ...

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  20. If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...

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