Derivative of ln(u) with respect to x | The Chain Rule Simplified

d/dx(lnu)

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

To find the derivative of ln(u) with respect to x, we can use the chain rule. The chain rule states that if we have a composition of functions, we can find the derivative by multiplying the derivative of the outer function with the derivative of the inner function.

In this case, the outer function is ln(u), and the inner function is u.

So, let’s start by finding the derivative of ln(u) with respect to u. The derivative of ln(u) with respect to u is 1/u. This is because ln(u) is the natural logarithm of u, and the derivative of ln(u) with respect to u is 1/u.

Next, we need to find the derivative of u with respect to x, denoted as du/dx. This represents how u changes as x changes.

Finally, we can multiply these two derivatives together:

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

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

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