How to Find the Derivative of ln(x) using the Chain Rule

(d/dx) lnx =

To find the derivative of ln(x) with respect to x, we can use the chain rule

To find the derivative of ln(x) with respect to x, we can use the chain rule.

Let’s first start by expressing ln(x) as y, so y = ln(x).

Now, we can take the derivative of both sides of this equation with respect to x:

d/dx (y) = d/dx (ln(x))

Using the chain rule, we can rewrite the derivative of y with respect to x as:

dy/dx = (dy/dx) * (dx/dx)

The derivative of y with respect to x is simply dy/dx, which is the same as d/dx (ln(x)).

The derivative of x with respect to x is 1, since any variable raised to the power of 1 is the variable itself.

Therefore, we have:

d/dx (ln(x)) = dy/dx = (dy/dx) * (dx/dx) = (d/dx) * (1)

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

Therefore, (d/dx) ln(x) = 1/x.

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