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
gilbertmuwowo35, let's knock this out. (d)/(dx) ( (x^2 + 3x - 4)/(x - 1) ) Step 1: Simplify the expression before differentiating. We can factor the numerator: x^2 + 3x - 4 = (x+4)(x-1). So, the expression becomes ((x+4)(x-1))/(x-1). For x ≠ 1, this simplifies to x+4. Step 2: Differentiate the simplified expression. We need to find the derivative of x+4 with respect to x. (d)/(dx)(x+4) = (d)/(dx)(x) + (d)/(dx)(4) Step 3: Apply the power rule and the constant rule for differentiation. The derivative of x (which is x^1) is 1 · x^1-1 = 1 · x^0 = 1. The derivative of a constant (4) is 0. Step 4: Combine the results. (d)/(dx)(x+4) = 1 + 0 = 1 The derivative of the given expression is 1. 1 Send me the next one 📸