How to Solve a Quotient Rule Derivative with Step-by-Step Guide

(1/u)(du/dx)

d/dx ln u

To solve this derivative, we can use the power rule of differentiation. Recall that if we have a function of the form f(x) = x^n, then its derivative is given by:

f'(x) = n * x^(n-1)

Now, let’s look at the given expression: (1/u)(du/dx)

We can see that this is a quotient, so we’ll need to use the quotient rule of differentiation. Recall that if we have a function of the form f(x) = u(x)/v(x), then its derivative is given by:

f'(x) = [u'(x)v(x) – u(x)v'(x)] / [v(x)]^2

Using this rule, we can find the derivative of our expression as follows:

(1/u)(du/dx) = [1 * u'(x) – u(x) * d/dx(1)] / [u(x)]^2

Since the derivative of a constant (1 in this case) is zero, we can simplify the right-hand side of the equation:

(1/u)(du/dx) = u'(x) / [u(x)]^2

Therefore, the derivative of (1/u)(du/dx) is equal to u'(x) / [u(x)]^2.

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