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.
-$$u ( 2 ) = 10 , u ^ { \prime } ( 2 ) = 4 , v ( 2 ) = - 3 , v ^ { \prime } ( 2 ) = - 5 \text {. }$$
$\frac { \mathrm { d } } { \mathrm { dx } } \left( \frac { \mathrm { v } } { \mathrm { u } } \right)$ at $\mathrm { x } = 2$
A) $- \frac { 31 } { 50 }$
B) $\frac { 19 } { 50 }$
C) $- \frac { 19 } { 50 }$
D) $- \frac { 19 } { 5 }$

Question

Quizplus · Accepted Answer

To find the derivative of $\frac{v}{u}$ with respect to $x$, we use the quotient rule: $\left(\frac{v}{u}\right)' = \frac{u'v - uv'}{u^2}$. Plugging in the given values at $x = 2$, we get $\frac{(4)(-3) - (10)(-5)}{10^2} = \frac{-12 + 50}{100} = \frac{38}{100} = -\frac{19}{50}$.

Suppose U and V Are Differentiable Functions of X u(2)=10,u′(2)=4,v(2)=−3,v′(2)=−5. u ( 2 ) = 10 , u ^ { \prime } ( 2 ) = 4 , v ( 2 ) = - 3 , v ^ { \prime } ( 2 ) = - 5 \text {. }u(2)=10,u′(2)=4,v(2)=−3,v′(2)=−5.

Suppose U and V Are Differentiable Functions of X $u ( 2 ) = 10 , u ^ { \prime } ( 2 ) = 4 , v ( 2 ) = - 3 , v ^ { \prime } ( 2 ) = - 5 \text {. }$