related rates

To solve related rates problems:

1. find out what related rate (derivative) the problem is looking for.
2. write out information given.
3. find out the relationship between variables.
4. fill out known values.
5. do necessary substitutions (e.g. $r\Rightarrow 4h$) (for cylinder problems) before differentiation.
6. do implicit differentiation (relative to some other variable, e.g. $x^2⟹2x\frac{dx}{dt}$ instead of just $2xdx$).
7. plug in the values, rearrange so that one side becomes the required related rate / derivative (e.g. $\frac{dx}{dt}$)