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.
-$$u ( 1 ) = 4 , u ^ { \prime } ( 1 ) = - 7 , v ( 1 ) = 7 , v ^ { \prime } ( 1 ) = - 3 \text {. }$$
$\frac { d } { d x } \left( \frac { u } { v } \right)$ at $x = 1$
A) $- \frac { 37 } { 7 }$
B) $- \frac { 61 } { 49 }$
C) $- \frac { 37 } { 9 }$
D) $- \frac { 37 } { 49 }$

Question

Quizplus · Accepted Answer

To find the derivative of $\frac{u}{v}$ with respect to $x$, we use the quotient rule: $\left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2}$. Plugging in the given values at $x = 1$, we get $\frac{(-7)(7) - (4)(-3)}{7^2} = \frac{-49 + 12}{49} = \frac{-37}{49}$.

Suppose U and V Are Differentiable Functions of X u(1)=4,u′(1)=−7,v(1)=7,v′(1)=−3. u ( 1 ) = 4 , u ^ { \prime } ( 1 ) = - 7 , v ( 1 ) = 7 , v ^ { \prime } ( 1 ) = - 3 \text {. }u(1)=4,u′(1)=−7,v(1)=7,v′(1)=−3.

Suppose U and V Are Differentiable Functions of X $u ( 1 ) = 4 , u ^ { \prime } ( 1 ) = - 7 , v ( 1 ) = 7 , v ^ { \prime } ( 1 ) = - 3 \text {. }$