" If "y=f(x)" is differential function of "x" then "(d^(2)x)/(d^(2)y)=

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

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

y=f(x) be a real valued twice differentiable function defined on R then (d^(2)y)/(dx^(2))((dx)/(dy))^(2)+(d^(2)x)/(dy^(2))=

The differentiation of y=a^x.

If y=f(x) is a differentiable function, then show that frac( d^2 x}{d y^2 } = (dy/dx)^3 . frac{ d^2 y}{d x^2 }

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 f(x) is a differentiable function for all x gt 0 and lim_(y to x)(y^(2)f(x)-x^(2)f(y))/(y-x)=2 , then the value of f'(x) is -

Differentiate the function f(x) = sqrt(x-2)

If y=f(x) is twice differentiable function such that at a point P,(dy)/(dx)=4,(d^2y)/(dx^2)=-3, then ((d^2x)/(dy^2))=