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Tamil Nadu Board of Secondary EducationHSC Science Class 12

For the following functions find the gxy, gxx, gyy and gyx g(x, y) = x2 + 3xy – 7y + cos(5x) - Mathematics

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Question

For the following functions find the gxy, gxx, gyy and gyx 

g(x, y) = x2 + 3xy – 7y + cos(5x)

Sum
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Solution

gx = `(del"g")/(delx) = 2x + 3y - 5 sin(5x)`

gy = `(del"g")/(dely) = 3x - 7`

gxx = `2 - 25 cos(5x)`

gyy = 0

gxy = `del/(delx) ((del"g")/(dely))`

= `del/(delx) (3x - 7)`

= 3

gyx = `del/(dely) ((del"g")/(delx))`

= `del/(dely) (2x + 3y - 5 sin(5x))`

= 3

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Partial Derivatives
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Chapter 8: Differentials and Partial Derivatives - Exercise 8.4 [Page 79]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board
Chapter 8 Differentials and Partial Derivatives
Exercise 8.4 | Q 5. (iii) | Page 79

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