Differentials ?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(? ) ? x. ? ? ? f(?x) = e? ^2?x

Solution 32E 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 Given the function f(x) = e2x Then f (x) = 2e2x Therefore dy = f (x)dx dy = 2e dx