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If f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x...

If `f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)ddot(cosn x+isinn x)` and `f(1)=1` , then `f"(1)` is equal to `(n(n+1))/2` (b) `{(n(n+1))/2}^2` (c) `-{(n(n+1))/2}^2` (d) none of these

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RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If x=t^2,\ \ y=t^3 , then (dy)/(dx)

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  2. If y=a+b x^2,\ a ,\ b arbitrary constants, then find dy/dx

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  3. If f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)ddot(cosn x+isinn x) a...

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  4. If y=asinm x+bcosm x , then find dy/dx

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  5. If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)= (a)1 (...

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  6. If y=tan^(-1){((log)e(e//x^2))/((log)e(e x^2))}+tan^(-1)((3+2\ (log)e ...

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  7. Let f(x) be a polynomial. Then, the second order derivative of f(e^...

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  8. If y=acos((log x)+bsin((log x) , then find dy/dx

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  9. If x=2 and y=a t^2 ,then find dy/dx

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  10. If x=f(t) and y=g(t) , then find (dy)/(dx)

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  11. If y=sin(m\ sin^(-1)x) , then (1-x^2)y2-x y1 is equal to m^2y (b) m y ...

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  12. If y=(sin^(-1)x)^2,\ then (1-x^2)y2 is equal to x y1+2 (b) x y1-2 (c)...

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  13. If y=e^(tanx) , then (cos^2x)y2-(1+sin2x)y1=0

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  14. If y=2/(sqrt(a^2-b^2)){tan^(-1)sqrt((a-b)/(a+b))tan(x/2)} , then show ...

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  15. If y=(a x+b)/(x^2+c), prove that (2x y1+y)y3=3(x y2+y1)y2.

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  16. If y=loge(x/(a+b x))^x , then x^3y2 is (a) (x y1-y)^2 (b) (1+y)^2 ...

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  17. If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ...

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  18. If y^(1/n)+y^(-1/n) = 2x then (x^2-1)y2+xy1 is equal to

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  19. differentiate y= sinx +logx with respect to x

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  20. If y=xlogx then find dy/dx

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