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`

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

Let u(x) a n dv(x) be differentiable functions such that (u(x))/(v(x))=7. (u^(prime)(x))/(v^(prime)(x))=pa n d((u(x))/(v(x)))'=q ,t h e n(p+q)/(p-q) has the value of to 1 (b) 0 (c) 7 (d) -7

If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2 , then find the value of f^(prime)(1) .

If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2 , then find the value of f^(prime)(1) .

If u = (x-3)/( 2) and v= ( y-2)/( 3), then cov(u,v) = k cov(x,y) . The value of k is

If u=sin^(-1)((2x)/(1+x^2)) and v=tan^(-1)((2x)/(1-x^2)) , where -1

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

If u=3x^(12) and v=x^(6) then (du)/(dv) is

Let u(x) and v(x) satisfy the differential equation (d u)/(dx)+p(x)u=f(x) and (d v)/(dx)+p(x)v=g(x) are continuous functions. If u(x_1) for some x_1 and f(x)>g(x) for all x > x_1, prove that any point (x , y), where x > x_1, does not satisfy the equations y=u(x) and y=v(x)dot

Find the polynomials u(x) and v(x) such that (x^(4) -1) * u(x) + (x^(7) -1) * v(x) = (x-1) .