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If f(x)=(cosx+isinx)(cos3x+isin3x)...(co...

If `f(x)=(cosx+isinx)(cos3x+isin3x)...(cos(2n-1)x+isin(2n-1)x)` then `f"(x)` is

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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)

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

Knowledge Check

  • The function f(x)=(cosx+isinx)(cos3x+isin3x)...{cos(2n-1)x+isin(2n-1)x} , then f'(x) is equal to

    A
    `n^2f(x)`
    B
    `-n^4f(x)`
    C
    `-n^2f(x)`
    D
    `n^4f(x)`

  • If f(x) = (cos x + i sin x)(cos 3x + i sin 3x) ….(cos (2n - 1)x + i(sin(2n - 1)x) , then f^(11)(x) is

    A
    `n^2f(x) `
    B
    `-n^(4)f(x)`
    C
    `-n^2f(x)`
    D
    `n^4f(x)`

  • 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^(2)f(x)`
    B
    `-n^(4)f(x)`
    C
    `-n^(2)f(x)`
    D
    `n^(4)f(x)`

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    If f(x)=(cos x+i sin x)(cos2x+i sin2x)(cos3x+i sin3x)......(cos nx+i sin n and f(1)=1, then f^(11) is equal to (a) (n(n+1))/(2) (b) {(n(n+1))/(2)}^(2)(C)-{(n(n+1))/(2)}^(2) (d) none of these

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