$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$

question 558

Multiple Choice

$$\text { Use implicit differentiation to find } d y / d x \text { and } \mathrm { d } ^ { 2 } y / d x ^ { 2 } \text {. }$$
- $$x ^ { 2 } + y ^ { 2 } = 4$$

• A) \(\frac { d y } { d x } = - \frac { x } { y } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = - \frac { x + y ^ { 2 } } { y ^ { 3 } }\)
• B) \(\frac { d y } { d x } = \frac { x } { y } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = \frac { x ^ { 2 } - y } { y ^ { 2 } }\)
• C) \(\frac { d y } { d x } = - \frac { x } { y } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = - \frac { x ^ { 2 } + y ^ { 2 } } { y ^ { 2 } }\)
• D) \(\frac { d y } { d x } = - \frac { x } { y } ; \frac { d ^ { 2 } y } { d x ^ { 2 } } = - \frac { x ^ { 2 } + y ^ { 2 } } { y ^ { 3 } }\)

---

Definitions:

Mixed Numbers

Numbers consisting of an integer and a proper fraction, representing sums of whole numbers and fractions.

Improper Fractions

Fractions where the numerator is greater than or equal to the denominator, representing a value of one or more.

Lowest Terms

The simplest form of a fraction, where the numerator and the denominator are reduced to their smallest whole numbers.

Quarts

A unit of volume in the U.S. customary and the British imperial systems, equal to a quarter of a gallon, or approximately 0.946 liters.