If `x=f(t), y=g(t)` are differentiable functions of parameter 't' then prove that y is a differentiable function of 'x' and
`(dy)/(dx)=((dy)/(dt))/((dx)/(dt)),(dx)/(dt) ne 0`
Hence find `(dy)/(dx)` if `x=a cos t, y= a sin t.`

Find (dy)/(dx) , if x=a t^2 , y=2a t

If x and y are differentiable functions of t, then (dy)/(dx)=(dy//dt)/(dx//dt)," if "(dx)/(dt)ne0 .

Find (dy)/(dx) , if x=a t^2, y=2a t .

If x = f(t) and y = g(t) are differentiable functions of t so that y is a differentiable functions of x and if dx//dt ne 0 then (dy)/(dx) =(dy)/((dt)/((dx)/(dt)) . Hence find dy/dx if x= 2sint and y=cos2t

Find (dy)/(dx) , if x=2a t^2 , y=a t^4

If x=f(t) and yy=g(t) are differentiable functions of t then (d^(2)y)/(dx^(2)) is

If y=f(x) is a differentiable function x such that invrse function x=f^(-1) y exists, then prove that x is a differentiable function of y and (dx)/(dy)=(1)/((dy)/(dx)) where (dy)/(dx) ne0 Hence, find (d)/(dx)(tan^(-1)x) .

If y = f(u) is a differentiable functions of u and u = g(x) is a differentiable functions of x such that the composite functions y = f[g(x) ] is a differentiable functions of x then (dy)/(dx) = (dy)/(du) . (du)/(dx) Hence find (dy)/(dx) if y = sin ^(2)x

If y =f(u) is differentiable function of u, and u=g(x) is a differentiable function of x, then prove that y= f [g(x)] is a differentiable function of x and (dy)/(dx)=(dy)/(du)xx(du)/(dx) .