Find the largest value of `a` such that there exists a differential function `y=f(x)`, for `-a

The largest value of c such that there exists a differentiable function f(x) for -c lt x lt c that satisfies the equation y_1 = 1+y^2 with f(0)=0 is (A) 1 (B) pi (C) pi/3 (D) pi/2

The largest value of c such that there exists a differentiable function f(x) for -c lt x lt c that satisfies the equation y_1 = 1+y^2 with f(0)=0 is (A) 1 (B) pi (C) pi/3 (D) pi/2

If y = f(x) is a differentiable function of x. Then-

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) .

Find the largest possible domain for the real valued functions f defined by f(x) = sqrt(x^2 - 5x + 6)

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(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) .

Find the largest possible domain for the real valued function f defined by f(x)=sqrt(x^(2)-5x+6) .

Find the largest possible domain for the real valued function f defined by f(x)=sqrt(x^(2)-4x+3) .