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 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=sin^(-1)((2x)/(1+x^(2)))andv=tan^(-1)((2x)/(1-x^(2))) , then (du)/(dv) is

If x+ y= (7)/(2) and xy= (5)/(2) , find x-y

If sin^(-1)((x^2-y^2)/(x^2+y^2))=logat h e n(dy)/(dx)i se q u a lto (x^2-y^2)/(x^2+y^2) (b) y/x (c) x/y (d) none of these

Let U=sin^(-1)((2x)/(1+x^2)) and V=tan^(-1)((2x)/(1-x^2)) , then (d U)/(d V)= (a) 1//2 (b) x (c) (1-x^2)/(1+x^2) (d) 1

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

find the following products (i) ((x)/(2)+2y)((x^(2))/(4)-xy+4y^(2)) (ii) (x^(2)-1)(x^(4)+x^(2)+1)

If u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt((1-u^2)/(1-v^2))

If u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt((1-u^2)/(1-v^2))