3.If` u=x^2y+y^2z+z^2x`, show that
`(delu)/(delx) + (delu)/(dely)+(delu)/(delz) = (x+y+z)^2`

If u=(x^(2)+y^(2)+z^(2))^(-1/2) show that x(del u)/(del x)+y(del u)/(del y)+z(del u)/(del z)=-u

If u=(x^(2)+y^(2)+z^(2))^(-1/2) show that x(del u)/(del x)+y(del u)/(del y)+z(del u)/(del z)=-u

If u= tan^-1((y^5)/(x^2)) , then find i. x((delu)/(delx)) + y((delu)/(dely)) ii. x^2((del^2u)/(delx^2))+2xy((del^2u)/(delxdely))+y^2((del^2u)/(dely^2))

If z(x+y)= x^2 +y^2 show that (frac{delz}{delx}-frac{del z}{del y})^2 = 4 (1- frac{delz}{delx}+frac{delz}{dely})

If a^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

If z= x + yi and |2z + 1| = |z- 2i| , show that 3(x^(2) + y^(2)) + 4(x-y)=3

If x,y,z gt 0 and x + y + z = 1, the prove that (2x)/(1 - x) + (2y)/(1 - y) + (2z)/(1 - z) ge 3 .

If x+y+z=x y z prove that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/(1-x^2)(2y)/(1-y^2)(2z)/(1-z^2)dot

For conservative force field, vec(F)=-(delU)/(delx)hat(i)-(delU)/(dy)hat(j)-(delU)/(delz)hat(k) where Frarr Maginitude of Force. Urarr Potential energy and (delU)/(delx)= Differentiation of U w.r.t. x keeping y and z constant and so on. Choose incorrect matching :-

Show that the plane x-5y-2z =1 contains the line (x-5)/3 = y = 2- z