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 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)=(d u)/(dx)v.w+u.(d v)/(dx).w+u.v(d w)/(dx) in two ways - first by repeated application of product rule, second by logarithmic differentiation.

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) .

If u=inte^(ax)sin " bx dx" and v=inte^(ax)cos " bx dx then "(u^(2)+v^(2))(a^(2)+b^(2))=

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

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

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

Verify the correctness of the equations v = u + at .

Let u(x) and v(x) are differentiable function such that (u(x))/(v(x))=6 . If (u'(x))/(v'(x))=p and ((u(x))/(v(x)))'=q then value of (p+q)/(p-q) is equal to