d/dx[lnx]
To find the derivative of ln(x), we can use the properties of logarithms and apply the chain rule, which states that if we have a function inside another function, we need to multiply the derivative of the outer function by the derivative of the inner function
To find the derivative of ln(x), we can use the properties of logarithms and apply the chain rule, which states that if we have a function inside another function, we need to multiply the derivative of the outer function by the derivative of the inner function.
The natural logarithm function, ln(x), can also be written as log_e(x), where e is Euler’s number, approximately 2.71828.
So, we can rewrite ln(x) as log_e(x) and differentiate it using the chain rule:
d/dx[ln(x)] = d/dx[log_e(x)]
To differentiate log_e(x) with respect to x, we consider the derivative of the logarithm function log_e(u):
d/dx[log_e(u)] = 1/u * du/dx
In our case, u = x:
d/dx[ln(x)] = 1/x * dx/dx
Now, dx/dx is equal to 1, so we have:
d/dx[ln(x)] = 1/x
Therefore, the derivative of ln(x) is 1/x.
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