Find the derivative of the function.
-$$r = \left( \frac { 1 + 7 \theta } { 7 \theta } \right) ( 7 - \theta )$$
A) $\frac { \mathrm { dr } } { \mathrm { d } \theta } = \frac { 1 } { \theta ^ { 2 } } + 1$
B) $\frac { d r } { d \theta } = \frac { 1 } { \theta ^ { 2 } } + 7$
C) $\frac { d r } { d \theta } = \theta ^ { 2 } - 1$
D) $\frac { d r } { d \theta } = - \frac { 1 } { \theta ^ { 2 } } - 1$

Question

Quizplus · Accepted Answer

First, simplify the given function: $r = \left( \frac { 1 + 7 \theta } { 7 \theta } \right) ( 7 - \theta ) = \left( \frac { 1 } { 7 \theta } + 1 \right) ( 7 - \theta ) = \frac { 7 } { 7 \theta } - \frac { \theta } { 7 \theta } + 7 - \theta = \frac { 1 } { \theta } + 7 - \theta$. Then, differentiate with respect to $\theta$: $\frac { d r } { d \theta } = - \frac { 1 } { \theta ^ { 2 } } - 1$.

Find the Derivative of the Function r=(1+7θ7θ)(7−θ)r = \left( \frac { 1 + 7 \theta } { 7 \theta } \right) ( 7 - \theta )r=(7θ1+7θ​)(7−θ)

Find the Derivative of the Function $r = \left( \frac { 1 + 7 \theta } { 7 \theta } \right) ( 7 - \theta )$