Implicit Differentiation w/ Composite Function

[Loppyfoot]

Homework Statement

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

The Attempt at a Solution

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

Would that be the correct way to begin this problem? Then plug in 3 for dx/dt and 1/2 for f'(x)?

Thanks

 

[Mark44]

Homework Statement

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

The Attempt at a Solution

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

Would that be the correct way to begin this problem? Then plug in 3 for dx/dt and 1/2 for f'(x)?

Thanks

Not quite.
You have
y = f(x), where both y and x are assumed (implicitly) to be functions of t. I could write this as y(t) = f(x(t)), which would make the dependence of y and x on t explicit

dy/dt = d/dt(f(x(t)) = f'(x(t)) dx/dt
Here I have used the chain rule.