Derivative of ln x
To find the derivative of ln x, we can use the definition of the derivative and the properties of logarithmic functions
To find the derivative of ln x, we can use the definition of the derivative and the properties of logarithmic functions.
Let’s start by using the definition of the natural logarithm:
ln x = loge x
where “loge” represents the base e logarithm.
Now, the derivative of ln x can be found by applying the chain rule. The chain rule states that if we have a composite function, for example, f(g(x)), then the derivative of this composite function is given by:
d/dx [f(g(x))] = f'(g(x)) * g'(x)
In this case, our composite function is f(g(x)) = ln x and g(x) = x. Therefore, the derivative of ln x can be written as:
d/dx [ln x] = (d/dx) [ln(x)] * (d/dx) [x]
Since the derivative of x with respect to x is 1, we can simplify the equation to:
d/dx [ln x] = (d/dx) [ln(x)] * 1
Now, let’s find the derivative of ln(x) with respect to x. The derivative of ln x with respect to x is given by:
(d/dx) [ln(x)] = 1/x
Therefore, the derivative of ln x is 1/x.
In summary, the derivative of ln x is 1/x.
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