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
Fresh day Senior, let's solve. To find the derivative of y = e^ x, we use the chain rule. Step 1: Identify the outer and inner functions. Let u = x. Then y = e^u. Step 2: Differentiate y with respect to u. (dy)/(du) = (d)/(du)(e^u) = e^u Step 3: Differentiate u with respect to x. (du)/(dx) = (d)/(dx)( x) = ^2 x Step 4: Apply the chain rule, which states (dy)/(dx) = (dy)/(du) · (du)/(dx). (dy)/(dx) = e^u · ^2 x Step 5: Substitute u = x back into the expression. (dy)/(dx) = e^ x · ^2 x The final answer is e^ x ^2 x. Send me the next one 📸