Question

For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.

$u\left(x\right)=x^2+x+1$

Short answer

The differential du in terms of the differential dxis $du=(2x+1)dx$.

Step-by-step solution

Step 1. Given Information

For given function u(x) we have to write the differential du in terms of the differential dx.

$u\left(x\right)=x^2+x+1$

Step 2. Now finding the differential du in terms of the differential dx.

$$\begin{gathered} u\left(x\right)=x^2+x+1 \\ \frac{du}{dx}=2x+1 \\ du=(2x+1)dx \end{gathered}$$