Related rates problem...I'M DYING!

[Guest]

Okay. Related rates. You must find a formula to relate the two quantities. Generally, related rates problems are story problems, so it's easy to pick and choose your formula. However, I've got this:

"If y = x^3 + 2x and dx/dt = 5, find dy/dt when x = 2."

What do I differentiate? What equation do I use to relate these?

Any and all help would be appreciated...

 

[galactus]

This is a related rates without the story.

\(\displaystyle \L\frac{dy}{dt}=3x^{2}\frac{dx}{dt}+2\frac{dx}{dt}\)

Sub in your data and solve.

 

[tkhunny]

y = x^3 + 2x

First derivative.

dy = [3*x^2 + 2]*dx

Really, that's all there is to it.