Question

Further differentiation:
http://prntscr.com/b7xhui
I'm not sure how to solve this question.

Answer 1

if y is the function of x,
how would you have differentiated y^2 ?

Answer 2

\[\frac{ d }{ dy } (y^2) \frac{ dy }{ dx }\]
\[= 2y \frac{ dy }{ dx }\] i think?

Answer 3

thats absolutely correct :)

if N,M are the function of 't',
how to differentiate
-3N^2 and M^2
?

Answer 4

If I differentiate the equation, I get this:
\[ - 9{N^2}\dot N + 2M\dot M = 0\]

Answer 5

see if you too get that ^^

Answer 6

next, it is suffice to substitute N=2, and M=1

Answer 7

\[\frac{ d }{ dN }(-3N^3)\frac{ dN }{ dt }+\frac{ d }{ dM }(M^2)\frac{ dM }{ dt }\]
\[= -9N^2\frac{ dN }{ dt }+ 2M \frac{ dM }{ dt }\]
ohh and then we sub in M = 1 and N = 2..
\[= -36\frac{ dN }{ dt }+ 2\frac{ dM }{ dt }\]

Answer 8

that is = 0 right?
because derivative of a constant -23 would be 0

Answer 9

yes!
so then,
\[\frac{ dN }{ dt } = 72\frac{ dM }{ dt }\]

Answer 10

so c = 72 :D

Answer 11

sure?

Answer 12

wait no.

Answer 13

0 = -36 a + 2b

2b = 36 a

...

Answer 14

error.
dN/dt = 1/18 (dM/dt)

Answer 15

yusss

Answer 16

thaankk you both ! ^_^

Answer 17

welcome ^_^