Math (Derivative)

Assume that x and y are both differentiable functions of t and the required values of dy/dt and dx/dt

xy=6

a) Find dy/dt, given x=8 and dx/dt=12

b) Find dx/dt, given x=1 and dy/dt=-8

I started with a and got dy/dt=dx/dt(-y/x)

Plugging with the given values leaves me with dy/dt=12(-y/8)

There's a y that is not given, how would I find out y in this case???

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  1. Finally figured out, simply plug the given x value into the original equation!

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  2. This leaves with

    dy/dt=12(-.75/8)

    dy/dt=-1.125

    dy/dt=-9/8

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  3. a) y = 6 x^-1
    ... dy/dt = -6 x^-2 dx/dt
    ... dy/dt = (-6 / 64) * 12

    b) missing y a typo?

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