AP EAMCET2001MathematicsDifferentiation
If u=e^ x^2-y^2 , then
Options
- Ax u_x=y u_y
- By u_x=x u u_y
- Cy u_x+x u_y=0
- Dx^2 u_y+y^2 u_x=0
Correct answer
C. y u_x+x u_y=0
Step-by-step solution
Given that, u=e^ x^2-y^2 On differentiating partially u_x=e^ x^2-y^2 (2 x) On differentiating partially w.r.t. y . aligned u_y & =e^ x^2-y^2 (-2 y) y u_x & =e^ x^2-y^2 2 x y x u_y & =e^ x^2-y^x (-2 x y) aligned On adding Eqs. (i) and (ii) y u_x+x u_y=0