Calculus [Implicit Differentiation]

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If √x+√y=10 and y(16)=36, find y'(16) by implicit differentiation.

If somebody could please help me by explaining how to solve this problem ! Thank you (:

  • Calculus [Implicit Differentiation] -

    just take d/dx of each term in the equation. (f+g)' = f' + g', so you can treat each term on its ow.

    Recall that dx/dx = 1, so

    √x+√y=10
    1/(2√x) dx/dx + 1/(2√y) dy/dx = 0
    1/(2√x) + 1/(2√y) y' = 0
    at x=16, y=36, so

    1/(2*4) + 1/(2*6) y' = 0
    y' = (-1/8) * 12 = -3/2

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