If $f ( x , y ) = \sin ( x ) + y ^ { 2 }$

question 24

Essay

If $f ( x , y ) = \sin ( x ) + y ^ { 2 }$ x(u, v)= uv and y(u, v)= u + 3v.
If H(u, v)= f(x(u, v), y(u, v)), what is H_v(0,-2)? Give your answer to 4 decimal places.

---

Definitions:

Anatomy

The branch of biology concerned with the study of the structure of organisms and their parts; a detailed examination of the physical structure of organisms.

Secondary Tissues

Tissues that are produced by the secondary growth of plants, including xylem and phloem, contributing to the increased thickness of stems and roots.

Agents Of Erosion

Natural forces like water, wind, ice, and gravity that physically or chemically break down and carry away Earth's surface material.

Ice

A solid state of water that occurs when it freezes, typically at or below 0°C (32°F).