To find the derivative of the quotient of two functions u(x) and v(x), we can use the quotient rule.
The quotient rule states that the derivative of u(x)/v(x) is:
[d(u(x)/v(x))/dx] = (v(x)(du/dx) – u(x)(dv/dx))/[v(x)]^2
So, applying the quotient rule to [u/v], we get:
[d(u/v)/dx] = [(v * du/dx) – (u * dv/dx)]/v^2
Therefore, the derivative of [u/v] with respect to x is [(v * du/dx) – (u * dv/dx)]/v^2.
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