`int(u(v(du)/(dx)-u(dv)/(dx)))/(v^(3))dx=`

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)) .

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

The function u=e^(x)sin x,v=e^(x)cos x satisfy the equation (a) v(du)/(dx)-u(du)/(dx)=u^(2)+v^(2)(b)(d^(2)u)/(dx^(2))=2v(c)d^(2)v())/(dx^(2))=-2u(d)(du)/(dx)+(dv)/(dx)=2v

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

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

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.

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

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(du)/(dx) in two ways-first by repeated application of product rule, second by logarithmic differentiation.

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.