If u and v are two differentiable functions of x and y = uv , prove that ,
`(y')/(y)=(u')/(u)+(v')/(v)`
where dash (') denotes derivative w.r.t.x.

If u and v are two differentiable functions of x show that, (d)/(dx)("tan"^(-1)(u)/(v))=(v (du)/(dx)-u(dv)/(dx))/(u^(2)+v^(2)) .

If y=u//v," where "u,v," are differentiable functions of x and "vne0," then: "u(dv)/(dx)+v^(2)(dy)/(dx)=

If u, v, w are three differentiable functions of x , prove that d/dx (uvw) = ((du)/dx)vw + u ((dv)/dx) w + uv ((dw)/dx) . Use this result to differentiate x^(3)(x^(2)+1)(x^(4)+1) w.r.t. x.

Prove that (d)/(dx)uv=u(dv)/(dx)+v(du)/(dx) .

Find the differentiation of y=sin u, u=x^2 w.r.t.x.

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

If u and v are two functions of x then prove that : int uv dx = u int v dx - int [ (du)/(dx) int v dx ] dx Hence, evaluate int x e^(x) dx

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