Property of logarithms
posted by Jen .
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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