Question

From \[v+x\frac{dv}{dx}=\frac{v\cos v+1}{\cos v}\], what is \[x\frac{dv}{dx}\]?

Options

• \[\cos v\]

• \[\frac{1}{\cos v}\]

• \[v\cos v+1\]

• \[\frac{v}{\cos v}\]

Answer 1

Subtract \[v\] from \[\frac{v\cos v+1}{\cos v}\]. Since \[v=\frac{v\cos v}{\cos v}\], the remaining expression is \[\frac{1}{\cos v}\].