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    second derivative

    2e^(4x^4) find second derivative
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sherwin1 View Post
    2e^(4x^4) find second derivative
    so if u is a function, d/dx e^u = u' e^u

    now we have y = 2e^(4x^4)
    => y'= 16x^3(2)e^(4x^4) = 32x^3 * e^(4x^4)

    now for the second derivative we need the product rule:

    => y'' = 96x^2 * e^(4x^4) + 32x^3(16x^3)e^(4x^4)
    => y'' = 96x^2 * e^(4x^4) + 512x^6 * e^(4x^4)
    => y'' = 32x^2 * e^(4x^4) * [3 + 16x^4]
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