OCR Core 3- Hard rates of change question (5marks)

Hey guys,

Could someone please help me with this question... It's doing my head in, and have spent the last 3 hours trying to solve it:/

Volume=pi(e^p + 4e^0.5p +p - 5)

It is given that the point P is moving in the positive y direction along y axis at constant rate of 0.2cm min^-1. Find the rate at which the volume of the sold is increasing at the instant when p=4.


So my working:

DV/DP = pi(4.e^4 + 2e^2 + 1) is what I get when I differentiate the volume.
The answer to this is 734.6... I multipliy this by 0.2 and should get DV/DT?

I am using DV/DT= DV/DP * DP/DT
The answer is 44, but my answer is not:/ How did they get 44!!!!!

WIll be forever in debt if you can help, and ofc REP+

Your dV/dP is wrong. It looks like you've managed to get your derivative of e^p as pe^p.

Your dV/dP is wrong. It looks like you've managed to get your derivative of e^p as pe^p.

It's wrong? I thought e^p would be pe^p when differentiating?

Nope, $\dfrac{d}{dx} e^x = e^x$.

In general, if you have $f(x) = e^{g(x)}$, then it's derivitive will be $f'(x) = g'(x)e^{g(x)}$

OMG THANK YOU SOO MUCH!!! ITS 3.28AM BUT you still helped me out!
Mate I owe you biggg time!!
Once again thanks, aha sooo stupid!!!

which paper is this