We can find the derivative of ln(x) using the rules of logarithmic differentiation.
ln(x) can be written as:
ln(x) = loge(x)
Now, let’s differentiate both sides of the equation with respect to x:
d/dx[ln(x)] = d/dx[loge(x)]
Using the chain rule:
d/dx[loge(x)] = 1/x * d/dx[x]
The derivative of x with respect to x is 1.
Therefore,
d/dx[loge(x)] = 1/x * 1
Simplifying:
d/dx[ln(x)] = 1/x
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