Posted by **Jen** on Friday, October 20, 2006 at 9:51pm.

Using property of logarithms, how do I prove derivative of ln(kx) is 1/x

First observe that ln(kx) = ln(k) + ln(x) then take derivatives. The ln(k) is simply a constant so it goes away. You could also derive it as

d/dx ln(kx) = 1/kx * k by the chain rule.

To see that the derivative of ln(x) is 1/x here's a brief proof.

If you have y=ln(x) then

e

^{y}=x Now find dx/dy to get

dx/dy = e

^{y} because

d/dy e

^{y} = e

^{y}
So 1/dx/dy = dy/dx = 1/e

^{y} = 1/x

This assumes that you know

d/du e

^{u} = e

^{u} which is easier to derive from the definition than d/dx ln(x).

what are you doing please give alghorthm problums

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