If two resistors with resistances $R_1$ and $R_2$ are connected in parallel then the total resistance $R$, measured in ohms, is given by $\frac{1}{R}=\frac{1}{R1}+\frac{1}{R2}$. If $R_1$ and $R_2$ are increasing at rates of o.3 ohms/second and 0.2 ohms/second, how fast is R changing when $R_1$=80 ohms and $R_2$=100 ohms?
[Math] Related Rates Word Problem Help
calculus
Best Answer
Hint: You know $\dfrac{dR_1}{dt}$ and $\dfrac{dR_1}{dt}$.
Differentiate your equation : $\frac{1}{R}=\frac{1}{R1}+\frac{1}{R2}$ with respect to $t$.
$\dfrac {dR}{dt}=d\frac{\dfrac{(R_1+R_2)}{R_1R_2}}{dt}$. You can get $\dfrac {dR}{dt}$
$d\dfrac{\frac{(R_1+R_2)}{R_1R_2}}{dt}= \dfrac{d}{dt}.\dfrac{(\dfrac{dR_1}{dt}+\dfrac{dR_2}{dt})-2(\dfrac{dR_1}{dt}.R_2+\dfrac{dR_2}{dt}.R_1)}{(R_1R_2)^2}$
Doesn't get more messier than this. ;).