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Let f(x) be a polynomial in x . Then the...

Let `f(x)` be a polynomial in `x` . Then the second derivative of `f(e^x)wdotrdottdotxi s` `f^(e^x)dote^x+f^(prime)(e^x)` `f^(e^x)dote^(2x)+f^(prime)(e^x)dote^(2x)` `f^(e^x)e^(2x)` (d) `f^(e^x)dote^(2x)+f^(prime)(e^x)dote^x`

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Knowledge Check

  • Let f (x) be a polynomial in x, then the second derivative of f(x^(e)) is

    A
    `f"(e^(x)).e^(x)+f'(e^(x))`
    B
    `f"(e^(x)).e^(2x)+f'(e^(x)).e^(2x)`
    C
    `f"(e^(x)).e^(2x)`
    D
    `f"(e^(x)).e^(2x)+f'(e^(x)).e^(x)`

  • The derivative of f(x) = e^(e^(x^(2))) is

    A
    `2x e^(x^(2))`
    B
    ` e^(e^(x^(2))) e^(x^(2))`
    C
    `2x e^(e^(x^(2))) e^(x^(2))`
    D
    None of these

  • If inte^(2x)f'(x)dx=g(x) , then int[e^(2x)f(x)+e^(2x)f'(x)]dx=

    A
    `1/2[e^(2x)f(x)-g(x)]+c`
    B
    `1/2[e^(2x)f(x)-g(x)]+c`
    C
    `1/2[e^(2x)f(2x)+g(x)]+c`
    D
    `1/2[e^(2x)f'(2x)+g(x)]+c`

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    The derivative of f(x)=e^(2x) is

    Let f(x) be a polynomial.Then,the second order derivative of f(e^(x)) is f(e^(x))e^(2x)+f'(e^(x))e^(x)( b) f(e^(x))e^(x)+f'(e^(x))(c)f(e^(^^)x)e^(^^)(2x)+f(e^(x))e^(x)(d)f(e^(x))

    " If f(x)=e^(2x-5) then f'(x) is

    f(x)=(e^(2x)-1)/(e^(2x)+1) is

    f(x)=((e^(2x)-1)/(e^(2x)+1)) is

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