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Math Help - derrivative

  1. #1
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    derrivative

    y=2^3x^2

    i dont know how to do this question at all, any help would be greatly appreciated.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by johntuan View Post
    y=2^3x^2

    i dont know how to do this question at all, any help would be greatly appreciated.
    And what is the question?

    Would it be: Find the dy/dx?

    y = 2^(3x^2)

    d/dx a^u = ln(a)*a^u *du/dx

    So,
    dy/dx = ln(2)*[2^(3x^2)]*6x
    dy/dx = 6ln(2)*x*2^(3x^2) ---------answer
    dy/dx = 6ln(2) *x *8^(x^2)
    dy/dx = ln(2^6) *x *8^(x^2)
    dy/dx = ln(64) *x *8^(x^2)

    ------------------
    Or,
    y = 2^(3x^2)
    y = (2^3)^(x^2)
    y = 8^(x^2)

    dy/dx = ln(8) *8^(x^2) *2x
    dy/dx = 2ln(8) *x *8^(x^2)
    dy/dx = ln(8^2) *x *8^(x^2)
    dy/dx = ln(64) *x *8^(x^2)
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