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 differentiate the given expression, we first simplify it by dividing each term in the numerator by the denominator. Step 1: Rewrite the expression by separating the terms. (6x^3 - 5x^2 + 1)/(3x^2) = (6x^3)/(3x^2) - (5x^2)/(3x^2) + (1)/(3x^2) Step 2: Simplify each term using the rules of exponents. = 2x^3-2 - (5)/(3)x^2-2 + (1)/(3)x^-2 = 2x^1 - (5)/(3)x^0 + (1)/(3)x^-2 Since x^0 = 1, the expression becomes: = 2x - (5)/(3) + (1)/(3)x^-2 Step 3: Differentiate each term with respect to x using the power rule (d)/(dx)(ax^n) = anx^n-1 and the rule that the derivative of a constant is zero. (d)/(dx)(2x - (5)/(3) + (1)/(3)x^-2) = (d)/(dx)(2x) - (d)/(dx)((5)/(3)) + (d)/(dx)((1)/(3)x^-2) = 2(1)x^1-1 - 0 + (1)/(3)(-2)x^-2-1 = 2x^0 - (2)/(3)x^-3 = 2(1) - (2)/(3)x^-3 = 2 - (2)/(3)x^-3 Step 4: Express the result with positive exponents. = 2 - (2)/(3x^3) The final answer is 2 - (2)/(3x^3). Send me the next one 📸