Let `g(x)` be the inverse of an invertible function `f(x),` which is differentiable for all real `xdot` Then `g^('')(f(x))` equals. (a)`-(f^('')(x))/((f^'(x))^3)` (b) `(f^(prime)(x)f^('')(x)-(f^(prime)(x))^3)/(f^(prime)(x))` (c)`(f^(prime)(x)f^('')(x)-(f^(prime)(x))^2)/((f^(prime)(x))^2)` (d) none of these

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

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

Let g(x) be the inverse of an invertible function f(x) which is differentiable at x=c . Then g'(f(x)) equal.(a) f'(c)( b) (1)/(f'(c)) (c) f(c) (d) none of these

Let g(x) be the inverse of the function f(x) ,and f'(x) 1/(1+ x^(3)) then g(x) equals

Let g(x) be the inverse of the function f(x) and f'(x)=(1)/(1+x^(3)) then g'(x) equals

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

Suppose fa n dg are functions having second derivative f'' and g' ' everywhere. If f(x)dotg(x)=1 for all xa n df^(prime)a n dg' are never zero, then (f^('')(x))/(f^(prime)(x))-(g^('')(x))/(g^(prime)(x))e q u a l (a)(-2f^(prime)(x))/f (b) (2g^(prime)(x))/(g(x)) (c)(-f^(prime)(x))/(f(x)) (d) (2f^(prime)(x))/(f(x))

Let f and g be function that are differentiable for all real numbers x and that have the following properties: f'(x)=f(x)-g(x)

If f(x)=|x-a|varphi(x), where varphi(x) is continuous function, then (a) f^(prime)(a^+)=varphi(a) (b) f^(prime)(a^-)=-varphi(a) (c) f^(prime)(a^+)=f^(prime)(a^-) (d) none of these