Let `g(x)` be the inverse of an invertible function `f(x)` which is derivable at `x=3` . If `f(3)=9` and `f^(prime)(3)=9` , write the value of `g^(prime)(9)` .

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 real xdot Then g''(f(x)) equals.

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

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 f(x) and f'(x)=1/(1+x^(3)) .Find g'(x) in terms of g(x).

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)4f(x_0),g^(prime)(x_0)=-7g(x_0), then the value of g^(prime)(1) is ________

If f(x)=a-(x-3)^(8//9) , then the maximum value of f(x) is

If y=f(x)=x^3+x^5 and g is the inverse of f find g^(prime)(2)

If is a real valued function defined by f(x)=x^2+4x+3, then find f^(prime)(1)a n df^(prime)(3)dot

If differentiable function f(x) in inverse of g(x) then f^(g(x)) is equal to (g^(x))/((g^(prime)(x))^3) 2. 0 3. (g^(x))/((g^(prime)(x))^2) 4. 1