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If f(x) is given by f(x)=(cosx+i sinx)...

If `f(x)` is given by
`f(x)`=`(cosx+i sinx)(cos3x+isin3x)......[cos(2n-1)x+isin(2n-1)x]`
then f''(x) is equal to
a. `n^(3)f(x)`
b. `-n^(4)f(x)`
c. `-n^(2)f(x)`
d. `n^(4)f(x)`

A

`n^(3)f(x)`

B

`-n^(4)f(x)`

C

`-n^(2)f(x)`

D

`n^(4)f(x)`

Text Solution

Verified by Experts

The correct Answer is:
B
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ARIHANT MATHS-DIFFERENTIATION -Exercise (More Than One Correct Option Type Questions)
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  2. If f(x) =|log(e)|x||, then f'(x) equals

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  3. If f(x) is given by f(x)=(cosx+i sinx)(cos3x+isin3x)......[cos(2n-1)...

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  4. Let f(x)=x^(n) , n being a non-negative integer, The value of n for w...

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  5. If f(x)=sin{(pi)/(3)[x]-x^(2)}" for "2ltxlt3 and [x] denotes the grea...

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  6. The functions u=e^(x).sinx and v=e^(x).cosx satisfy the equation

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  7. If f(x)=log(x^(2))(logx),then f '(x)at x= e is

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  8. Let f be a differentiable function satisfying [f(x)]^(n)=f(nx)" for ...

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  9. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

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  10. "If "y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo))))," then prove that "(dy)/(...

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  11. If f(x)=|cosx-sinx| , then f'(pi/4) is equal to

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  12. Let f(x)=x^2+xg'(1)+g''(2) and g(x)=f(1).x^2+xf'(x)+f''(x), then find ...

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  13. if f(x) = x^n then the value of f(1) - (f'(1))/(1!) + (f''(1))/(2!) +...

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  14. If y+log(1+x)=0 which of the following is true?

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  15. If y=2^(3^(x)), then y' equals

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  16. If g is the inverse of fandf(x) = x^(2)+3x-3,(xgt0). then g'(1) equal...

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  17. If x^(3)-2x^(2)y^(2)+5x+y-5=0 and y(1) = 1, then a. y'(1)=(4)/(3) b. y...

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  18. Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to

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  19. Ify=x^((lnx)^ln(lnx)) , then (dy)/(dx) is equal to

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  20. Which of the following functions are not derivable at x=0?

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