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`

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

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.

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) .

If x=sint and y=cos2t , then (dy)/(dx) =

y=t^(2)/(sqrt(t)) then find dy/dt

If y=a sin t, x=a cos t then find (dy)/(dx) .

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 x=t log t ,y =t^(t) ,then (dy)/(dx)=