Suppose u and v are differentiable functions of x. Use the given values of the functions and their derivatives to find the
value of the indicated derivative.
-$$u ( 1 ) = 5 , u ^ { \prime } ( 1 ) = - 5 , v ( 1 ) = 6 , v ^ { \prime } ( 1 ) = - 2 \text {. }$$
$\frac { d } { d x } \left( \frac { u } { v } \right)$ at $x = 1$
A) $- \frac { 10 } { 9 }$
B) $- \frac { 10 } { 3 }$
C) $- 5$
D) $- \frac { 5 } { 9 }$

Question

Quizplus · Accepted Answer

Using the quotient rule, 
$$\frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v\cdot u'-u\cdot v'}{v^2}$$
Substituting the given values, we get
$$\frac{d}{dx} \left( \frac{u}{v} \right) \Bigg|_{x=1} = \frac{(6)(-5) - (5)(-2)}{(6)^2} = - \frac{5}{9}$$
Therefore, the answer is D.

Suppose U and V Are Differentiable Functions of X u(1)=5,u′(1)=−5,v(1)=6,v′(1)=−2. u ( 1 ) = 5 , u ^ { \prime } ( 1 ) = - 5 , v ( 1 ) = 6 , v ^ { \prime } ( 1 ) = - 2 \text {. }u(1)=5,u′(1)=−5,v(1)=6,v′(1)=−2.

Suppose U and V Are Differentiable Functions of X $u ( 1 ) = 5 , u ^ { \prime } ( 1 ) = - 5 , v ( 1 ) = 6 , v ^ { \prime } ( 1 ) = - 2 \text {. }$