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`

If f(x)=x+tanx and f is inverse of g, then g ′(x) is equal to

If g is the inverse of a function f and f'(x) = 1/(1+x^(5)) , then g'(x) is equal to

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

f is a strictly monotonic differentiable function with f^(prime)(x)=1/(sqrt(1+x^3))dot If g is the inverse of f, then g^(x)= a. (2x^2)/(2sqrt(1+x^3)) b. (2g^2(x))/(2sqrt(1+g^2(x))) c. 3/2g^2(x) d. (x^2)/(sqrt(1+x^3))

If g(x)=1+sqrtx and f(g(x))=3+2sqrtx+x then f(x) is equal to

If f(x)=(x+3)/(5x^2+x-1) and g(x)=(2x+3x^2)/(20+2x-x^2) such that f(x) and g(x) are differentiable functions in their domains, then which of the following is/are true (a) 2f^(prime)(2)+g^(prime)(1)=0 (b) 2f^(prime)(2)-g^(prime)(1)=0 (c) f^(prime)(1)+2g^(prime)(2)=0 (d) f^(prime)(1)-2g^(prime)(2)=0

Suppose f and g are functions having second derivative f'' and g' ' everywhere. If f(x)dotg(x)=1 for all x and f^(prime) and g' are never zero, then (f^('')(x))/(f^(prime)(x))-(g^('')(x))/(g^(prime)(x)) is equal (a) (-2f^(prime)(x))/f (b) (2g^(prime)(x))/(g(x)) (c) (-f^(prime)(x))/(f(x)) (d) (2f^(prime)(x))/(f(x))

If f(x)a n dg(f) are two differentiable functions and g(x)!=0 , then show trht (f(x))/(g(x)) is also differentiable d/(dx){(f(x))/(g(x))}=(g(x)d/x{f(x)}-g(x)d/x{g(x)})/([g(x)]^2)

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

If f(x) = 3x + 1 and g(x) = x^(2) - 1 , then (f + g) (x) is equal to