Question

(2)
a(u, v)
If u = x² - y2 and v = 2xy then the value of is ..
a(x, y)
(A) 4(x² + y2)
(B) - 4(x² + y2
a(x,y)
(C) 4(x2 - y2)
(D) 0
If y
banhe​

Answer 1

$\displaystyle \sf{ \frac{ \partial (u,v)}{ \partial (x,y)} } = 4( {x}^{2} + {y}^{2} )$

Given :

u = x² - y² and v = 2xy

To find :

The value of ∂(u,v)/∂(x,y) is

(A) 4(x² + y²)

(B) - 4(x² + y²)

(C) 4(x² - y²)

(D) 0

Solution :

Step 1 of 2 :

Write down the functions

Here the given functions are

u = x² - y² and v = 2xy

Step 2 of 2 :

Find the value of ∂(u,v)/∂(x,y)

$\displaystyle \sf{ \frac{ \partial (u,v)}{ \partial (x,y)} }$

$\displaystyle = \begin {vmatrix} \frac{ \partial \sf u}{ \partial \sf x} & \frac{ \partial \sf v}{ \partial \sf x} \\ \\ \frac{ \partial \sf u}{ \partial \sf y} & \frac{ \partial \sf v}{ \partial \sf y} \end{vmatrix}$

$\displaystyle = \begin {vmatrix} \sf \:2x & \sf \:2y \\ \\ \sf \: - 2y & \sf \:2x \end{vmatrix}$

$\displaystyle \sf{ = 4 {x}^{2} + 4 {y}^{2} }$

$\displaystyle \sf{ = 4( {x}^{2} + {y}^{2} )}$

Hence the correct option is (A) 4(x² + y²)

Correct question :

If u = x² - y² and v = 2xy then the value of ∂(u,v)/∂(x,y) is

(A) 4(x² + y²) (B) - 4(x² + y²) (C) 4(x2 - y²) (D) 0