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Chapter 12: TF. 2 (page 946)

Achainruleforfunctionsoftwovariables:Letf(x,y)=x2y3,x=scost,andy=ssint.Find鈭�x鈭�sand鈭�x鈭�t.

Short Answer

Expert verified

鈭�x鈭�s=cost鈭�x鈭�t=-ssint

Step by step solution

01

Step 1. Given information

f(x,y)=x2y3,x=scost,andy=ssint.

02

Step 2. Finding partial derivatives

x=scost鈬�鈭�x鈭�s=cost鈬�鈭�x鈭�t=-ssint

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Most popular questions from this chapter

In Exercises 37-42, use the partial derivatives of gx,y=xcosyand the point 1,蟺specified to

afind the equation of the line tangent to the surface defined by the function in the xdirection,

bfind the equation of the line tangent to the surface defined by the function in the ydirection, and

cfind the equation of the plane containing the lines you found in parts aand b.

Describe the meanings of each of the following mathematical expressions:

鈭�w鈭�z

Explain the steps you would take to find the extrema of a function of two variablesf(x,y),if (x,y)is a point in a triangle role="math" localid="1649884242530" Tin the xy-plane.

Prove that if you minimize the square of the distance from the origin to a point (x, y) subject to the constraint g(x,y)=0, you have minimized the distance from the origin to (x, y) subject to the same constraint.

Evaluate the following limits, or explain why the limit does not exist.

lim(x,y)鈫�(4,蟺)tan-1yx
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