d/dx ln(x)
To find the derivative of ln(x) with respect to x, we can use the chain rule, which states that if we have a composition of functions, we take the derivative of the outer function and multiply it by the derivative of the inner function
To find the derivative of ln(x) with respect to x, we can use the chain rule, which states that if we have a composition of functions, we take the derivative of the outer function and multiply it by the derivative of the inner function.
In this case, the outer function is ln(u) and the inner function is x. So, let’s apply the chain rule:
d/dx ln(x) = (1/x) * d/dx x
The derivative of x with respect to x is simply 1. Therefore, we can simplify the equation to:
d/dx ln(x) = 1/x
So, the derivative of ln(x) with respect to x is 1/x.
Definition:
The natural logarithm, denoted as ln(x), is the logarithm to the base of ‘e’, where ‘e’ is the mathematical constant approximately equal to 2.71828. It is the inverse function of the exponential function, and it measures the time it takes for a quantity to grow exponentially. The logarithm tells us the exponent to which the base must be raised to obtain a certain value.
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