d(lnx)/dx
1/x
To find the derivative of ln(x) with respect to x, we use the chain rule of differentiation since the natural logarithm function is a composite function of e^x, where e is the Euler’s number. So, we have:
d/dx [ln(x)] = d/dx [e^(ln(x))] (using the inverse property of natural log)
Now, applying the chain rule, we get:
d/dx [e^(ln(x))] = e^(ln(x)) * d/dx [ln(x)]
Since e^(ln(x)) simplifies to x, we can substitute this value and continue our differentiation:
x d/dx [ln(x)]
Using the logarithmic differentiation rule, we can simplify this to:
d/dx [ln(x)] = 1/x
Therefore, the derivative of ln(x) with respect to x is 1/x.
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