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

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

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

Find dy/dx if : y=(3-v)/(2+v),v = (4x)/(1-x^2)

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

State true or false for the following statements : (d)/(dx)((u)/(v))=(v(du)/(dx)-u(dv)/(dx))/(v)

Let u(x) and v(x) be differentiable functions such that (u(x))/(v(x))=7 If (u^(prime)(x))/(v^(prime)(x))=p and ((u(x))/(v(x)))^'=q ,then (p+q)/(p-q) has the value (a) 1 (b) 0 (c) 7 (d) -7

Let the sides of a parallelogram be U=a, U=b,V=a' and V=b', where U=lx+my+n, V=l'x+m'y+n'. Show that the equation of the diagonal through the point of intersection of U=a, V=a' and U=b, V=b' " is given by " |{:(U,V,1),(a,a',1),(b,b',1):}| =0.