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.
-$$\begin{array} { l }
u ( 1 ) = 2 , u ^ { \prime } ( 1 ) = - 5 , v ( 1 ) = 7 , v ^ { \prime } ( 1 ) = - 4 \text {. } \
\frac { d } { d x } ( \text { uv } ) \text { at } x = 1
\end{array}$$
A) -38
B) 27
C) 43
D) -43

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.
-$$\begin{array} { l } 
u ( 1 ) = 2 , u ^ { \prime } ( 1 ) = - 5 , v ( 1 ) = 7 , v ^ { \prime } ( 1 ) = - 4 \text {. } \
\frac { d } { d x } ( \text { uv } ) \text { at } x = 1
\end{array}$$
A) -38
B) 27
C) 43
D) -43

Quizplus · Accepted Answer

Using the product rule, $\frac{d}{dx}(uv)=u'v+uv'$. Substituting the given values, $\frac{d}{dx}(uv)|_{x=1}=u'(1)v(1)+u(1)v'(1)=(-5)(7)+(2)(-4)=-43$. Therefore, the answer is (D).

Suppose U and V Are Differentiable Functions of X A) -38 B) 27 C) 43 D) -43

Suppose U and V Are Differentiable Functions of X A) -38
B) 27
C) 43
D) -43