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# Differentiation watch

1. x = a/(1 + kt) where a and k are constants.

Show that dx/dt = -kx2/a
2. rewrite as a(1+kt)^-1

then
dx/dt= -ak(1+kt)^-2

but x= a(1+kt)^-1 so you get
= -ak*x²/a² -- (we dont want a² because squaring x gives a²(1+kt)^-2 and we only want (1+kt)^-2 )
= -kx²/a
3. (Original post by Aired)
x = a/(1 + kt) where a and k are constants.

Show that dx/dt = -kx2/a
I would say:

1 + kt = a/x (now differentiate both sides with respect to t)

k = [-a/(x^2)]*(dx/dt) (by the chain rule)

therefore:

-kx2/a = dx/dt
4. (Original post by Aired)
x = a/(1 + kt) where a and k are constants.

Show that dx/dt = -kx2/a

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