Understanding the Derivative of ln(u) Using the Chain Rule! Boost Your Math Knowledge!

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To find the derivative of ln(u), we can use the chain rule of differentiation

To find the derivative of ln(u), we can use the chain rule of differentiation.

Let’s assume that u is a differentiable function of x. Then, we can write ln(u) as ln(f(x)) = ln(u(x)).

According to the chain rule, the derivative of ln(u) with respect to x is given by:

d/dx ln(u) = (d/dx ln(u(x))) * (du(x)/dx)

Now, let’s find the derivative of ln(u(x)) and du(x)/dx separately.

The derivative of ln(u(x)) can be found using the chain rule. Let v = u(x), then:

d/dx ln(u(x)) = d/dx ln(v) = (1/v) * (dv/dx)

Here, dv/dx is the derivative of v = u(x) with respect to x.

Next, we find the derivative of u(x) with respect to x, du(x)/dx.

Combining these derivatives, we get:

d/dx ln(u) = (1/u) * (du/dx)

So, the derivative of ln(u) with respect to x is (1/u) * (du/dx).

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