Chapter 6.4, Problem 39E

To determine

To calculate: The expression equivalent to $u^{\prime }\left(x\right)$, where $u\left(x\right)$ is the integrating factor for the differential equation $y^{\prime }+P\left(x\right)y=Q\left(x\right)$. The expressions in the options are:

(a)$P\left(x\right)u\left(x\right)$

(b)$P^{\prime }\left(x\right)u\left(x\right)$

(c)$Q\left(x\right)u\left(x\right)$

(d)$Q^{\prime }\left(x\right)u\left(x\right)$