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
To find the derivative of y=c from first principles, where c is a constant, we use the definition: f'(x) = _h 0 (f(x+h) - f(x))/(h) Step 1: Identify f(x) and f(x+h). Given f(x) = c. Since c is a constant, its value does not change with x. Therefore, f(x+h) = c. Step 2: Substitute f(x) and f(x+h) into the first principles formula. f'(x) = _h 0 (c - c)/(h) Step 3: Simplify the numerator. f'(x) = _h 0 (0)/(h) Step 4: Evaluate the limit. For any h ≠ 0, (0)/(h) = 0. The limit of 0 as h approaches 0 is 0. f'(x) = 0 The derivative of y=c is 0. That's 2 down. 3 left today — send the next one.