This is Differential Geometry explain and solve make sure the answer is correct

9. Consider a uniform cable with density hanging in equilibrium. As shown in Figure 1.12, the tension forces T(x 4+ Ax), T(x). and the weight of the piece of cable lying over [x, x + Ax] all balance. If the bottom of the cable is at x = 0, Ty is the magnitude of the tension there, and the cable is X X+ Ax FIGURE 1.12 the graph y = f(x), show that f"(x) = ';?T*\" + f'(x)2. (Remember that tanf = f'(x).) Letting 0 du C = Ty/g, show that f(x) = C cosh(x,/C)+c for some constant . (Hint: To integrale[ _ V14 u? make the substitution = sinh v.)