How to Find the Derivative of the Natural Logarithm of x with Respect to x

(d/dx) (logx) =

To find the derivative of the natural logarithm of x with respect to x, we use the logarithmic differentiation formula:

(d/dx) (logx) = 1/x

Here’s a step-by-step explanation:

Step 1: Start with the function f(x) = log(x)

To find the derivative of the natural logarithm of x with respect to x, we use the logarithmic differentiation formula:

(d/dx) (logx) = 1/x

Here’s a step-by-step explanation:

Step 1: Start with the function f(x) = log(x).

Step 2: Apply the logarithmic differentiation formula, which states that if f(x) = log(g(x)), then (d/dx) (log(g(x))) = (1/g(x)) * (d/dx) (g(x)).

In this case, g(x) = x. So we have f(x) = log(x) and g(x) = x.

Step 3: Take the derivative of g(x) with respect to x, which is just 1 (since the derivative of x with respect to x is 1).

Step 4: Substitute the values from steps 2 and 3 into the logarithmic differentiation formula:

(d/dx) (log(x)) = (1/x) * 1

Step 5: Simplify the expression:

(d/dx) (log(x)) = 1/x

So, the derivative of log(x) with respect to x is 1/x.

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