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calculus

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A. find y' by implicit differentiation.
B. solve th equation explicitly for y and differentiate to get y' in terms of x.

cos (x) + √y = 5

  • calculus -

    a)
    - sin(x) + (1/2)y^(-1/2)dy/dx = 0
    -(1/4)(1/√y)dy/dx = sin(x)

    dy/dx = -4√y sin(x)

    b)
    √y = 5 - cosx
    y = 25 - 10cosx + cos^2 x
    dy/dx = -10cosx + 2(cosx)(-sinx)
    = -2cosx(5cos(x) + 2sin(x))

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