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
Welcome back Alaks — missed you this week. Here's a breakdown of the calculation for the derivative of y = ^-1 x: Step 1: Rewrite the inverse function. If y = ^-1 x, then by definition of the inverse sine function, we can write x in terms of y: x = y Step 2: Differentiate x with respect to y. We differentiate both sides of x = y with respect to y: (dx)/(dy) = (d)/(dy)( y) = y Step 3: Express y in terms of x. We use the trigonometric identity ^2 y + ^2 y = 1. From this, we can express y as: y = sqrt(1 - ^2 y) Since we know x = y, we can substitute x for y: y = sqrt(1 - x^2) Step 4: Substitute y back into (dx)/(dy). Now we replace y in our expression for (dx)/(dy): (dx)/(dy) = sqrt(1 - x^2) Step 5: Find (dy)/(dx) using the reciprocal rule. To find (dy)/(dx), we use the reciprocal relationship between derivatives: (dy)/(dx) = (1)/(dx)dy Substitute the expression for (dx)/(dy): (dy)/(dx) = (1)/(sqrt(1 - x^2)) The final answer is: (dy)/(dx) = (1)/(sqrt(1 - x^2)) Drop the next question 📸