This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.
ScanSolve AI Answer
To find (dy)/(dx) for y = _e ((1)/(x)), we will use the chain rule. Step 1: Define a substitution for the inner function. Let u = (1)/(x). Then y = _e u. Step 2: Differentiate y with respect to u. (dy)/(du) = (d)/(du)(_e u) = (1)/(u) Step 3: Differentiate u with respect to x. We can write u = x^-1. (du)/(dx) = (d)/(dx)(x^-1) = -1 · x^-1-1 = -x^-2 = -(1)/(x^2) Step 4: Apply the chain rule formula (dy)/(dx) = (dy)/(du) × (du)/(dx). (dy)/(dx) = ((1)/(u)) × (-(1)/(x^2)) Step 5: Substitute u = (1)/(x) back into the expression for (dy)/(dx). (dy)/(dx) = ((1)/(1)x) × (-(1)/(x^2)) (dy)/(dx) = (x) × (-(1)/(x^2)) (dy)/(dx) = -(x)/(x^2) (dy)/(dx) = -(1)/(x) Comparing this result with the given options, the correct option is A. The final answer is A. -(1)/(x). Send me the next one 📸