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
5. Given y = xsqrt(x), find (d^2y)/(dx^2). Step 1: Rewrite the function y in exponential form. y = x · x^1/2 = x^1 + 1/2 = x^3/2 Step 2: Find the first derivative (dy)/(dx). Apply the power rule (d)/(dx)(x^n) = nx^n-1. (dy)/(dx) = (3)/(2)x^(3)/(2)-1 = (3)/(2)x^1/2 Step 3: Find the second derivative (d^2y)/(dx^2). Differentiate (dy)/(dx) again using the power rule. (d^2y)/(dx^2) = (d)/(dx)((3)/(2)x^1/2) = (3)/(2) · (1)/(2)x^(1)/(2)-1 (d^2y)/(dx^2) = (3)/(4)x^-1/2 Step 4: Express the result with a positive exponent. (d^2y)/(dx^2) = (3)/(4sqrt(x)) The final answer is (3)/(4sqrt(x)). 3 done, 2 left today. You're making progress.