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
The first principal derivative of x is found using the limit definition of the derivative: (d)/(dx)( x) = _h 0 ((x+h) - x)/(h) Step 1: Use the logarithm property a - b = (a)/(b). _h 0 ((x+h)/(x))h Step 2: Rewrite the expression inside the logarithm. _h 0 ((1 + h)/(x))h Step 3: Rearrange the expression to use the limit _u 0 ((1+u))/(u) = 1. Let u = (h)/(x). As h 0, u 0. We need to manipulate the expression to match this form. _h 0 (1)/(x) · ((1 + h)/(x))(h)/(x) Step 4: Apply the limit. (1)/(x) · _u 0 ((1+u))/(u) (1)/(x) · 1 Step 5: Simplify. (1)/(x) The first principal derivative of x is (1)/(x). Send me the next one 📸