# Thread: Comparison of Two Derivatives

1. ## Comparison of Two Derivatives

There's this equation that I have stumbled whilst working on several exercise questions.

I'm sorry that I post this in image, I've tried to write it down using Latex but it shows Error in preview mode.

The instruction is compare the derivative of P in respect to t with the derivative of P in respect to D. I have tried to solve it but my end calculation shows 9/DT instead of what it is supposed to be in the answer key, which is -D/T. I'm a bit confused here, what I'm doing wrong?

Thank You

2. I'm going call the stuff within the parentheses for A since it does not depend on t or D.

Then we have $\displaystyle \frac{dP}{dt}=\frac{3At^2}{D^3}$ and $\displaystyle \frac{dP}{dD}=\frac{-3At^3}{D^4}$

Comparing the two we see that $\displaystyle \frac{-D}{t}\cdot \frac{dP}{dD}=\frac{3At^2}{D^3}=\frac{dP}{dt}$

3. Originally Posted by Mondreus
I'm going call the stuff within the parentheses for A since it does not depend on t or D.

Then we have $\displaystyle \frac{dP}{dt}=\frac{3At^2}{D^3}$ and $\displaystyle \frac{dP}{dD}=\frac{-3At^3}{D^4}$

Comparing the two we see that $\displaystyle \frac{-D}{t}\cdot \frac{dP}{dD}=\frac{3At^2}{D^3}=\frac{dP}{dt}$
Ah ok thanks, I forgot to add the minus in differentiating the D^3.