Derivative of ln x
1/x
The derivative of ln x is simply 1/x. To find the derivative of ln x using calculus, we can use the logarithmic differentiation technique.
Let y = ln x. Taking the natural logarithm of both sides, we have:
ln y = ln(ln x)
Differentiating both sides with respect to x:
(1/y)dy/dx = 1/x * 1/ln x
Simplifying this expression, we get:
dy/dx = y/x
Substituting y = ln x, we get:
dy/dx = (ln x)/x
Therefore, the derivative of ln x is 1/x.
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