IF f and g are prime numbers, what is `f+g`?

If f,g, and h are differentiable functions of x and (delta) = |[f,g,h], [(xf)',(xg)',(xh)'],[(x^2f)' ',(x^2g)' ',(x^2h)' ']| prove that delta^(prime) = |[f,g,h],[f',g', h],[ (x^3f' ')',(x^3g' ')',(x^3h ' ')']|

If f,g, and h are differentiable functions of x and (delta) = |[f,g,h], [(xf)',(xg)',(xh)'],[(x^2f)' ',(x^2g)' ',(x^2h)' ']| prove that delta^(prime) = |[f,g,h],[f',g', h],[ (x^3f' ')',(x^3g' ')',(x^3h ' ')']|

For a twice differentiable function f(x),g(x) is defined as g(x)=f^(prime)(x)^2+f^(prime)(x)f(x)on[a , e]dot If for a

If f(x) and g(x) are be two functions with all real numbers as their domains, then h(x) =[f(x) + f(-x)][g(x)-g(-x)] is:

Let f(x)=sqrtx and g(x)=x be two functions defined over the set of non-negative real numbers. Find (f+g) (x), (f-g), (fg) (x) and (f/g) (x) .

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))

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)=(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

If f(g(x)) = g(f(x)) = x for all real numbers x, and f(2) = 5 and f(5) = 3, then the value of g(3)+ g(f(2)) is