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Calculus

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find y' if sin^-1(xy)=cosy

  • Calculus -

    Use implicit differentiation:
    sin^-1(xy)=cosy
    sin(cos(y))=xy
    differentiate both sides with respect to x
    (use chain rule):
    cos(cos(y))(-sin(y))y'=y+xy'
    Collect terms and solve for y'
    y'=-y/(cos(cos(y))sin(y)+x)

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