The derivative of natural logarithm of x (ln x) can be found as follows:
Let y = ln x, where x > 0
Taking the exponential of both sides, we have:
e^y = e^{ln(x)} = x
Differentiating both sides with respect to x:
d/dx [e^y] = d/dx [x]
Using the chain rule and the fact that d/dx e^y = e^y, we get:
e^y(dy/dx) = 1
Therefore, dy/dx = 1/x
So, the final answer is:
d/dx [ln x] = 1/x
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