If g is inverse of f then prove that `f''(g(x))=-g''(x)(f'(g(x)))^(3).`

If g is inverse of function f and f'(x)=sinx , then g'(x) =

If g is the inverse of f and f'(x)=(1)/(1+x^(n)) prove that g'(x)=1+(g(x))^(n)

If g is the inverse function of and f'(x) = sin x then prove that g'(x) = cosec (g(x))

If g is the inverse function of and f'(x) = sin x then prove that g'(x) = cosec (g(x))

If g is the inverse function of and f'(x) = sin x then prove that g'(x) = cosec (g(x))

If g(x) is the inverse function and f'(x) = sin x then prove that g'(x) = cosec [g(x)]

Let f(x) and g(x) be two function having finite nonzero third-order derivatives f''(x) and g''(x) for all x in R. If f(x)g(x)=1 for all x in R, then prove that (f''')/(f')-(g'')/(g')=3((f'')/(f)-(g'')/(g))

If g is the inverse of f and f(x)=(1)/(1+x^(3)) then g'(x)=

If f(x)=x^(3)+3x+4 and g is the inverse function of f(x), then the value of (d)/(dx)((g(x))/(g(g(x)))) at x = 4 equals

If f(x)=x^(3)+3x+4 and g is the inverse function of f(x), then the value of (d)/(dx)((g(x))/(g(g(x)))) at x = 4 equals