If `y=(u)/(v)`, where u and v are functions of x, show that
`v^(3)(d^(2)y)/(dx^(2))=|{:(u,v,0),(u',v',v),(u'',v'',2v'):}|`.

If u, v and w are functions of x, then show that (d)/(dx) (u.v.w) = (du)/(dx) v.w + u.(dv)/(dx).w + u.v.(dw)/(dx) in two ways- first by repeated application of product rule, second by logarithmic differentiation. Using product rule

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

If (x, y) and (X, Y) be the coordinates of the same point referred to two sets of rectangular axes with the same origin and if ux + vy , when u and v are independent of X and Y become VX + UY, show that u^(2)+v^(2)=U^(2)+V^(2) .

Let u(x) and v(x) be differentiable functions such that (u(x))/(v(x))=7.if(u'(x))/(v'(x))=pand((u(x))/(v(x)))'=q," then "(p+q)/(p-q) has the value equal to

Find the dimensions of a in the formula (p+a/V^2)(V-b)=RT

If the readings V_(1) and V_(3) are 10. volt each, then reading of V_(2) is:

Find the points of discontinuity of y = (1)/(u^(2) + u -2) , where u = (1)/(x -1)

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