?Consider the following functions and express the relationship between a small change in x and the corresponding change in y in the form dy = ?f?? ?dx?. f? ?)= (4 +? ?)/(4 ? ?x?)

Solution 34E STEP 1 Let f be the function differentiable on an interval containingx.The small change in x is denoted by the differential dx. The corresponding change in f is approximated by the differential dy = f x)dx STEP 2 4+x Given the function f(x) = 4x By Quotient rule we get Then f (x) = (4x)(1)(4+x)(=) 4x+4+x = 8 (4x)2 (4x) (4x) Therefore dy = f ()dx dy = 8 2 dx (4x)