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.
-$$\begin{array} { l }
u ( 1 ) = 4 , u ^ { \prime } ( 1 ) = - 6 , v ( 1 ) = 6 , v ^ { \prime } ( 1 ) = - 3 \
\frac { d } { d x } ( u v ) \text { at } x = 1
\end{array}$$
A) -48
B) -42
C) 24
D) 48

Question

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.
-$$\begin{array} { l } 
u ( 1 ) = 4 , u ^ { \prime } ( 1 ) = - 6 , v ( 1 ) = 6 , v ^ { \prime } ( 1 ) = - 3 \
\frac { d } { d x } ( u v ) \text { at } x = 1
\end{array}$$
A) -48
B) -42
C) 24
D) 48

Quizplus · Accepted Answer

Using the product rule, we have$$\frac{d}{dx}(uv) = u\frac{dv}{dx} + v\frac{du}{dx}$$Substituting the given values, we get$$\frac{d}{dx}(uv) \bigg|_{x=1} = (4)(-3) + (6)(-6) = -12 - 36 = -48$$Therefore, the answer is A.

Suppose U and V Are Differentiable Functions of X A) -48 B) -42 C) 24 D) 48

Suppose U and V Are Differentiable Functions of X A) -48
B) -42
C) 24
D) 48