Mastering the chain rule of calculus: Solving problems with functions of x

(1/u ln a)(du/dx)

d/dx log a u

To solve this problem, we need to use the chain rule of calculus, which states that if we have a function g(u) where u is a function of x, then:

d/dx [g(u)] = g'(u) * du/dx

In this case, we can see that we have a function f(u) = ln a, where u is a function of x. Using the chain rule, we can write:

d/dx [ln a/u] = (1/u) * du/dx (since the derivative of ln a is 0)

Now we can substitute our expression for d/dx [ln a/u] into the original problem:

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

This is our final answer.

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