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Math Help - calculus AB test practice problems

  1. #1
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    Exclamation calculus AB test practice problems

    if y=x^(x^3), then dy/dx=

    a.) x^(x^3 +2) (2+3lnx)
    b.) x^(x^3+2)
    c.) 4x^(x^3+2)
    d.) x^3 (l+3lnx)
    e.) (lnx)x^(x^3)
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  2. #2
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    Quote Originally Posted by andyaddition View Post
    if y=x^(x^3), then dy/dx=

    a.) x^(x^3 +2) (2+3lnx)
    b.) x^(x^3+2)
    c.) 4x^(x^3+2)
    d.) x^3 (l+3lnx)
    e.) (lnx)x^(x^3)
    Re-write the function:

    y=x^{x^3} = e^{\ln(x) \cdot x^3}

    Use chain rule. For the derivation of the exponent you have to use the product rule.

    The solution is a).
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  3. #3
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    Quote Originally Posted by andyaddition View Post
    if y=x^(x^3), then dy/dx=

    a.) x^(x^3 +2) (2+3lnx)
    Should be x^(x^3 +2) (1+3lnx)
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  4. #4
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    yes thank you very much
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