Calculate the Derivative of the Function $$\left. \frac { \mathrm { dr } } { \mathrm { d } \theta } \right| _ { \theta = 3 } \text { if } \mathrm { r } = \frac { 4 } { \sqrt { 12 - \theta } }$$

question 116

Multiple Choice

Calculate the derivative of the function. Then find the value of the derivative as specified.
- $$\left. \frac { \mathrm { dr } } { \mathrm { d } \theta } \right| _ { \theta = 3 } \text { if } \mathrm { r } = \frac { 4 } { \sqrt { 12 - \theta } }$$

• A) \(\frac { \mathrm { dr } } { \mathrm { d } \theta } = - \frac { 2 } { ( 12 - \theta ) ^ { 3 / 2 } } ; \frac { \mathrm { d } r } { \mathrm {~d} \theta } \mid \theta = 3 = - \frac { 2 } { 27 }\)
• B) \(\frac { \mathrm { dr } } { \mathrm { d } \theta } = \frac { 2 } { ( 12 - \theta ) ^ { 3 / 2 } } ; \left. \frac { \mathrm { dr } } { \mathrm { d } \theta } \right| _ { \theta = 3 } = \frac { 2 } { 27 }\)
• C) \(\frac { \mathrm { dr } } { \mathrm { d } \theta } = \frac { 4 } { ( 12 - \theta ) ^ { 3 / 2 } } ; \left. \frac { \mathrm { dr } } { \mathrm { d } \theta } \right| _ { \theta = 3 } = \frac { 4 } { 27 }\)
• D) \(\frac { \mathrm { dr } } { \mathrm { d } \theta } = - \frac { 4 } { ( 12 - \theta ) ^ { 3 / 2 } } ; \frac { \mathrm { dr } } { \mathrm { d } \theta } \mid \theta = 3 = - \frac { 4 } { 27 }\)

---

Definitions:

Truck Data Bus

A communication system within a truck that allows for the exchange of data between electronic control units (ECUs) and devices.

Vehicle Computer Processing

The computing systems within a vehicle that manage various functions such as engine operation, navigation, and infotainment.

Algorithm

Software term that describes a programmed sequence of operating events; the rules and conditions for producing a processing outcome from a computer. This is also known by some OEMs as mapping.

Cycle

A sequence of operations or events that repeats, such as in machinery operation, biological processes, or computational logic.