# Thread: Hard but Easy Implicit Differentiation Related Rate Composite Function

1. ## 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?
Danke schön!

2. Originally Posted by r2d2
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.

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