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Math Help - Hard but Easy Implicit Differentiation Related Rate Composite Function

  1. #1
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    Hard but Easy Implicit Differentiation Related Rate Composite Function

    Given y=f(x) , at a certain point the slope of the curve is 1/2 and the x-coordinate is decreasing at the rate of 3 units/s. At that point, how fast is the y-coordinate of the object changing?

    So would the problem start like this?:

    dy/dt= f'(x) dx/dt

    Plug in 1/2 for f'(x)
    Plug in 3 units/s for dx/dt.

    Would this be correct to find dy/dt?
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  2. #2
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    Quote Originally Posted by r2d2 View Post
    Given y=f(x) , at a certain point the slope of the curve is 1/2 and the x-coordinate is decreasing at the rate of 3 units/s. At that point, how fast is the y-coordinate of the object changing?

    So would the problem start like this?:

    dy/dt= f'(x) dx/dt

    Plug in 1/2 for f'(x)
    Plug in 3 units/s for dx/dt.

    Would this be correct to find dy/dt?
    Danke schön!
    Yes, that is correct.

    f'(x) = \frac{dy}{dx} so \frac{dy}{dt} = \frac{dy}{dx} \times \frac{dx}{dt} = f'(x) \times \frac{dx}{dt}
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