Mastering The Chain Rule: How To Find The Derivative Of Ln(U) With Respect To X

d/dx(lnu)

u’/u

To find the derivative of ln(u) with respect to x, we’ll need to use the chain rule.

Let’s begin by defining a new function v = u(x). Then we have

y = ln(v)

Now we can use the chain rule, which says that

dy/dx = dy/dv * dv/dx

The first factor is easy to find, since the derivative of ln(v) with respect to v is simply 1/v:

dy/dv = 1/v

The second factor is also straightforward, since we defined v = u(x):

dv/dx = du/dx

Putting it all together, we have:

dy/dx = dy/dv * dv/dx
= (1/v) * (du/dx)
= (1/u(x)) * (du/dx)

So finally we can write:

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

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

More Answers: