If $f$ Is the Focal Length of a Convex Lens and an and an Object

Multiple Choice

If $f$ is the focal length of a convex lens and an object is placed at a distance $v$ from the lens, then its image will be at a distance $u$ from the lens, where $f , v$ , and $u$ are related by the lens equation $\frac { 1 } { f } = \frac { 1 } { v } + \frac { 1 } { u } .$
Find the rate of change of $v$ with respect to $u$ .

A) $\frac { d v } { d u } = - \frac { f } { ( u - f ) ^ { 2 } }$
B) $\frac { d v } { d u } = - \frac { f ^ { 2 } } { u - f }$
C) $\frac { d v } { d u } = \frac { 2 f ^ { 2 } } { ( u - f ) ^ { 2 } }$
D)
$$\frac { d v } { d u } = \frac { f ^ { 2 } } { ( u - f ) ^ { 2 } }$$
E)
$$\frac { d v } { d u } = - \frac { f ^ { 2 } } { ( u - f ) ^ { 2 } }$$