Use Logarithmic Differentiation to Find the Derivative of Y with Respect

question 51

Multiple Choice

Use logarithmic differentiation to find the derivative of y with respect to the independent variable.
- $$y = 4 t \sqrt { t }$$

• A) \(\frac { 4 t \sqrt { t } + 1 ( \ln 4 t ) } { \sqrt { t } + 1 }\)
• B) \(4 t \left( \frac { 1 } { 2 } \ln 4 t + 1 \right)\)
• C) \(\frac { 1 } { \sqrt { t } } \left( \frac { 1 } { 2 } \ln 4 t + 1 \right)\)
• D) \(\frac { 4 \mathrm { t } \sqrt { \mathrm { t } } } { \sqrt { \mathrm { t } } } \left( \frac { 1 } { 2 } \ln 4 \mathrm { t } + 1 \right)\)

---

Definitions:

Cuddliness

The quality of being affectionate and huggable, often used to describe how comfortable and comforting something or someone feels.

Anesthetics

Substances used to induce loss of sensation or consciousness during medical procedures.

Sedatives

Sedatives are a class of drugs that slow brain activity, used for calming the nervous system and inducing sleep or relaxation.

Pain Medication

Drugs or substances specifically used to relieve pain, ranging from over-the-counter analgesics to prescription opioids.