5. The first derivate of a function f is defined by f (x) = lim f(xth)-f(x) . where f (x) is the h-0 h slope of the tangent line to the function f at x. Use the above f (x) to prove the following questions. (a) If f is a constant function, i.e. f (x) = c, where c is a constant. Then, f (x) = 0 (b) The first derivative of a function of (x), where c is a constant, is of (x). (c) Now, let's define g (x) = lim g(xth)-g(x) h ', where g (x) is the slope of the tangent line to a function g at x. Consider the function F(x) = f(x) + g(x). Show that the first derivative of the function F(x), F'(x) , is equal to f (x) + g (x) (d) Consider the function F(x) = f(x) x g(x). Show that the first derivate of the function F(x), F (x), is equal to f (x) x g'(x)+f (x) xg(x)