Property of logarithms

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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
ey=x Now find dx/dy to get
dx/dy = ey because
d/dy ey = ey
So 1/dx/dy = dy/dx = 1/ey = 1/x

This assumes that you know
d/du eu = eu 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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