Derivative of ln x
The derivative of ln x (the natural logarithm of x) can be found using the chain rule of differentiation
The derivative of ln x (the natural logarithm of x) can be found using the chain rule of differentiation.
Let’s start by differentiating the natural logarithm function, which is given by y = ln x.
Using the definition of the natural logarithm, we can write x = e^y. Now, take the derivative of both sides with respect to x:
1 = (e^y) * dy/dx
Since we want to find dy/dx, we rearrange the equation:
dy/dx = 1 / (e^y)
But we know that x = e^y, so we can substitute this back in:
dy/dx = 1 / x
Therefore, the derivative of ln x with respect to x is 1/x.
In mathematical notation, we can write:
d/dx (ln x) = 1/x
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