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 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 and int uv dx=phi(x)-int[(du)/(dx)intv dx]dx , then the value of phi(x) is-

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.

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 (a) 1 (b) 0 (c) 7 (d) -7

If y=e^u and u=f(x) , show that, (d^2y)/(dx^2)=e^u[(d^2u)/(dx^2)+((du)/dx)^2]

If y = e^u and u = f(x), show that, (d^2y)/(dx^2) = e^u [(d^2u)/(dx^2) + ((du)/(dx))^2] .

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

Differentiate the following functions w.r.t. x : (tan x )/(x)log (e^(x)/(x^(x)))

Differentiate the following functions w.r.t. x : e^(x)tan x

Differentiate the following functions w.r.t. t : (u)/( e^(u) -1)