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William
William asked in Science & MathematicsMathematics · 3 years ago

finding the derivative problem I posted a picture please help?

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2 Answers

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  • Ash
    Lv 7
    3 years ago

    y = (3-x²)^½

    dy/dx = ½(3-x²)^⁻½ d/dx (3-x²)

    dy/dx = ½(3-x²)^⁻½ (-2x)

    dy/dx = -x(3-x²)^⁻½

    A = -1

    B = -½

    d²y/dx² = -x d/dx((3-x²)^⁻½) + (-1)(3-x²)^⁻½

    d²y/dx² = -x(-½) (3-x²)^(-3/2) d/dx(3-x²) - (3-x²)^-½

    d²y/dx² = -x(-½) (3-x²)^(-3/2) (-2x) - (3-x²)^-½

    d²y/dx² = - (3-x²)^-½ - x²(3-x²)^(-3/2)

    C = -1

    D = -½

    F = -1

    G = 2

    H = -3/2

  • hayharbr
    Lv 7
    3 years ago

    Chain rule

    Let u = 3 - x^2

    y = u ^ 1/2

    dy/dx = dy/du • du/dx

    = 1/2 u ^ -1/2 • -2x

    = -x u ^ -1/2

    = -x(3 - x^2) ^ -1/2

    A = -1

    Then use product rule with another chain rule

    I got (but you should check because I already found one mistake)

    C = -1

    D = -1/2

    F = -1

    G = 2

    H = -3/2

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