Question

For the substitution \[y=vx\], which differentiated form is correct?

Options

• \[\frac{dy}{dx}=x\frac{dv}{dx}\]

• \[\frac{dy}{dx}=v+x\frac{dv}{dx}\]

• \[\frac{dy}{dx}=\frac{dv}{dx}+xv\]

• \[\frac{dy}{dx}=v+y\frac{dv}{dy}\]

Answer 1

With \[y=vx\], both \[v\] and \[x\] occur in a product. Using the product rule gives \[\frac{dy}{dx}=v+x\frac{dv}{dx}\].