This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey Nurse, good to see you again. The given function is y = 8e^x^3. To find the derivative (dy)/(dx), we will use the chain rule. Step 1: Identify the outer and inner functions. Let u = x^3. Then the function becomes y = 8e^u. Step 2: Differentiate the outer function with respect to u and the inner function with respect to x. The derivative of y = 8e^u with respect to u is (dy)/(du) = 8e^u. The derivative of u = x^3 with respect to x is (du)/(dx) = 3x^2. Step 3: Apply the chain rule, which states (dy)/(dx) = (dy)/(du) · (du)/(dx). (dy)/(dx) = (8e^u) · (3x^2) Step 4: Substitute u = x^3 back into the expression and simplify. (dy)/(dx) = 8e^x^3 · 3x^2 (dy)/(dx) = 24x^2 e^x^3 The derivative of the function is: 24x^2 e^x^3 What's next? 📸