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Chapter 12: Q. 23 (page 944)

Use the definition of the partial derivative to find the partial derivatives specified in Exercises 23鈥�26.

fy2,1when localid="1650225390806" fx,y=9-x2-y2.

Short Answer

Expert verified

The partial derivative is-2.

Step by step solution

01

Given

The given function is:fx,y=9-x2-y2.

02

To find

We have to findfy2,1.

03

Calculation

Differentiate both sides with respect toyand then plug x = 2 and y = 1.

fx,y=9-x2-y2fyx,y=鈭�鈭�y9-x2-y2fyx,y=0-0-2yfyx,y=-2yfy2,1=-21fy2,1=-2

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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.

Sketch the level curves f(x, y) = c of the following functions for c = 鈭�3, 鈭�2, 鈭�1, 0, 1, 2, and 3:

f(x,y)=x鈭�sin鈭�1鈦�y

Gradients: Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.

f(x, y ,z) = ln(x + y + z), P = (e, 0, 鈭�1) .

Use Theorem 12.32 to find the indicated derivatives in Exercises 21鈥�26. Express your answers as functions of a single variable.

d胃dtwhen胃=tan鈭�1yx,x=et,andy=e2t

Describe the meanings of each of the following mathematical expressions :

fyx0,y0
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