[ejwm]

Here's the question:
the variables x and t are such that the rate of increase of lnx with respect to t is proportional to x.
a) express this statement as an equation, and hence show that the rate of increase of x with respect to t is proportional to x^2.

I got that dlnx/dt = kx

but how do you do show dx/dt =kx^2?

thanks

[f1mad]

Differentiate lnx with respect to t.

I.e d(lnx)/dt

[ejwm]

(Original post by f1mad)
Differentiate lnx with respect to t.

I.e d(lnx)/dt

How would you do that?

[aznkid66]

It should be in a formula packet, if not memorized.

lnx=t
x=e^t

dx/dt=e^t, t=lnx
dt/dx=...

[f1mad]

(Original post by ejwm)
How would you do that?

Try that for instead of

[Zuzuzu]

(Original post by ejwm)
Here's the question:
the variables x and t are such that the rate of increase of lnx with respect to t is proportional to x.
a) express this statement as an equation, and hence show that the rate of increase of x with respect to t is proportional to x^2.

I got that dlnx/dt = kx

but how do you do show dx/dt =kx^2?

thanks

You have d/dt lnx = kx and d/dx lnx = 1/x, so combining these...

[ejwm]

(Original post by f1mad)




Try that for instead of

thank you so much