Let `f(x)` be differentiable function and `g(x)` be twice differentiable function. Zeros of `f(x),g^(prime)(x)` be `a , b` , respectively, `(a

if f(x) be a twice differentiable function such that f(x) =x^(2) " for " x=1,2,3, 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) .

If both f(x)&g(x) are differentiable functions at x=x_(0) then the function defiend as h(x)=Maximum{f(x),g(x)}

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all x, then g'f(x) is equal to

A function f(x) is differentiable at x=c(c in R). Let g(x)=|f(x)|,f(c)=0 then

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

Let f : (a, b) to R be twice differentiable function such that f(x) = int _(a) ^(x) g (t) dt for a differentiable function g(x) . If f(x) = 0 has exactly five distinct roots in (a,b) , then g(x) g'(x) = 0 has at least

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all real x. Then g''(f(x)) equals

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then