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 u=f(x-y,y-z,z-x) , prove that (partialu)/(partialx)+(partialu)/(partialy)+(partialu)/(partialz)=0 .

If (x+yi)^(3)=u + vi , prove that (u)/(x) +(v)/(y) = 4(x^(2)-y^(2))

If x+ yi= (u+ vi)/(u-yi) , prove that x^(2) + y^(2)=1

If u = x^(2) + y^(2) " and " x = s + 3t, y = 2s - t , " then " (d^(2) u)/(ds^(2)) is equal to

The function u=e^x sin x ; v=e^x cos x satisfy the equation a. v(d u)/(dx)-u(d v)/(dx)=u^2+v^2 b. (d^2u)/(dx^2)=2v c. (d^2v)/(dx^2)=-2u d. (d u)/(dx)+(d v)/(dx)=2v

Show that the equation, y=a sin(omegat-kx) satisfies the wave equation (del^(2) y)/(delt^(2))=v^(2) (del^(2)y)/(delx^(2)) . Find speed of wave and the direction in which it is travelling.

If (x+i y)^3=u+i v , then show that u/x+v/y=4(x^2-y^2)

If (x+i y)^3=u+i v , then show that u/x+v/y=4(x^2-y^2) .