Derivative of ln x
The derivative of ln(x) can be found using the properties of logarithmic differentiation
The derivative of ln(x) can be found using the properties of logarithmic differentiation.
To begin, we write ln(x) as the natural logarithm of x:
ln(x) = log_e(x)
Where log_e represents the logarithm with base e.
Now, let’s find the derivative of ln(x) with respect to x:
d/dx [ln(x)]
Using the chain rule for differentiation, we let u = ln(x) and differentiate it with respect to u:
du/dx = 1/x
Now, we can find dx/dx by differentiating x with respect to x, which is simply 1:
dx/dx = 1
Applying the chain rule, we can express the derivative of ln(x) as:
d/dx [ln(x)] = du/dx * dx/dx
= (1/x) * 1
= 1/x
Therefore, the derivative of ln(x) is 1/x.
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