I can't seem to get the correct answer for this problem:
A particle is moving along the curve $y=4\sqrt{4x+5}.$ As the particle
passes through the point $(5,20),$ its $x$-coordinate increases at a rate
of $2$ units per second. Find the rate of change of the distance from
the particle to the origin at this instant.
Here's my attempt at the problem (I'm not sure where I went wrong):
Thanks for your help!
Best Answer
Your formula for $\frac{dy}{dt}$ is incorrect. You forgot the apply one instance of the chain rule, to take the derivative of $4x+5$, so you are missing a factor of $4$. Or something like that, since you apparently corrected the $2$ to a $4$, but it should have been $8$. It should be
$$\begin{align} \frac{dy}{dt} &= \frac d{dt}\left(4\sqrt{4x+5}\right) \\[3 ex] &= 4\frac{1}{2\sqrt{4x+5}}\cdot 4\frac{dx}{dt} \\[2 ex] &= \frac{8}{\sqrt{4x+5}}\frac{dx}{dt} \end{align}$$
You can continue from there.