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Math

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Find the derivative: y = square root of x(x+14).

The square root is only on the x. Please show work and explain. I don't know how to do this. Thanks!

  • Math -

    if y = √u = u^(1/2)
    y' = 1/2 * u^(-1/2) u'

    u = x^2+14x
    u' = 2x+14

    y' = (2x+14)/(2√x(x+14))
    = (x+7)/√x(x+14)

  • Math - Oops -

    oops. I didn't read it carefully

    use the product rule: if
    y = f*g, y' = f'*g + f*g'

    y = (x+14)√x
    y' = (1)√x + (x+14)*(1/2√x)
    = (2x+x+14)/2√x
    = (3x+14)/2√x

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