Question

Find the rate of change of q with respect to p when:
p=20/(q^2+5)

I get 40q'/(y^2+5)^2 but alas, my answer choices are -10/(qp^2), -5/(q^2p), -10/(qp), -5/(qp)^2. I think it's the last one but i'm not sure.

Answer 1

why do you have a "y" in your answer?

Answer 2

sorry it should say q

Answer 3

those are your choices? wow.

Answer 4

you are looking for
\[q'\] right?

Answer 5

yeah, I really hate this program we use it simplifies it
in odd ways to trick you.

Answer 6

lets try this and see if it works

Answer 7

yes, with respect to p

Answer 8

start with
\[p=\frac{20}{q^2+5}\]
\[p(q^2+5)=20\]
\[pq^2+5p=20\] now take the derivative of q wrt p using implicit differentiation

Answer 9

you get
\[q^2+2pqq'=5=20\] and now solve for
\[q'\]

Answer 10

ok that is a typo let me write it correctly

Answer 11

you get
\[q^2+2pqq'+5=0\]

Answer 12

so
\[2pqq'=-5-q^2\]
\[q'=\frac{-5-q^2}{2pq}\] is that one of the answers?

Answer 13

no, I was thinking it was the last one. There was also a 'none of theese' answer but I selected it and got it wrong

Answer 14

ok lets try this
\[p=\frac{20}{q^2+5}\]
\[\frac{20}{p}=q^2+5\]
\[q^2=\frac{20}{p}+5\] and now take the derivative

Answer 15

get
\[2qq'=-\frac{20}{p^2}\]
\[q'=-\frac{10}{qp^2}\] is that one?

Answer 16

yes

Answer 17

well maybe it is right. one can only hope

Answer 18

It was right! Thank you. Can you help me with one more?