Question

For the substitution \[x=vy\], which differentiated form is correct?

Options

• \[\frac{dx}{dy}=y\frac{dv}{dy}\]

• \[\frac{dx}{dy}=v+x\frac{dv}{dx}\]

• \[\frac{dx}{dy}=v+y\frac{dv}{dy}\]

• \[\frac{dx}{dy}=\frac{dv}{dy}+yv\]

Answer 1

With \[x=vy\], differentiate with respect to \[y\]. The product rule gives \[\frac{dx}{dy}=v+y\frac{dv}{dy}\].