Consider the following limit. lim u+ 5 U- -5 us + 125 Simplify the rational expression as much as possible. lim U - -5 Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) X 2) If f is a differentiable function, find an expression for the derivative of each of the following functions. (a) y = x ((x) Oy' = x 5f' ( x ) + 5x # [(x ) Oy' = x"f' ( x) - 4x5((x ) Oy = x 5 ((x ) + 5x " f" ( x ) Oy' = x 5(( x ) - 5x 4 f" ( x ) Oy' = x* f (x ) + 4x5((x ) (b) y = ( x) x4 Or = xf' (x ) + 31(x) x 4 Oy = *f'(x) - 4f(x) x 5 Oy' = X(x) - 4f'(x) Oy = Xf'(x) - 3/(x) Oy' = *f(x) + 4f' (x) (c) y = x 7( x ) Oy' = 1(x)(7x8 ) + x8," (x ) [1(x)12 Oy = f'(x)(8x') - x8((x) [((x)12 Oy = (x)(8x') - x8,' (x) [1(x)12 Oy = f(x)(7x') - x8," (x) [(x)12 Oy = f'(x)(7x8) + x'((x) [f(x)12 (d) y =- 9 + xf (x ) V x Oy' = xf'(x) + 9x2((x) - 2 2x3/2 Oy' = Xf ( x) + 2x2f' (x) - 9 2x 3/2 Oy' = *f(x) + 9x2 ((x) - 2 2x3/2 Oy' = x(x) - 9x2f'(x) + 9 2x 3/2 Oy' = xf' (x) - 2x2 f' (x ) + 9 2x3/2