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 y = x^3 - (2)/(x^3) - 2 with respect to x, we can rewrite the expression using negative exponents. Step 1: Rewrite the function. y = x^3 - 2x^-3 - 2 Step 2: Apply the power rule for differentiation, (d)/(dx)(x^n) = nx^n-1, and the rule that the derivative of a constant is 0. (dy)/(dx) = (d)/(dx)(x^3) - (d)/(dx)(2x^-3) - (d)/(dx)(2) (dy)/(dx) = 3x^3-1 - 2(-3)x^-3-1 - 0 (dy)/(dx) = 3x^2 + 6x^-4 Step 3: Rewrite the term with the negative exponent as a fraction. (dy)/(dx) = 3x^2 + (6)/(x^4) That's 2 down. 3 left today — send the next one.