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
Here's the derivative for the given function: Given y = 2e^x + 3 x - 5 + (1)/(x^2) Step 1: Rewrite the expression, converting the fraction to a term with a negative exponent. y = 2e^x + 3 x - 5 + x^-2 Step 2: Differentiate each term using the following rules: • (d)/(dx)(e^x) = e^x • (d)/(dx)( x) = (1)/(x) • (d)/(dx)(c) = 0 (for a constant c) • (d)/(dx)(x^n) = nx^n-1 (dy)/(dx) = (d)/(dx)(2e^x) + (d)/(dx)(3 x) - (d)/(dx)(5) + (d)/(dx)(x^-2) (dy)/(dx) = 2e^x + 3((1)/(x)) - 0 + (-2)x^-2-1 (dy)/(dx) = 2e^x + (3)/(x) - 2x^-3 Step 3: Rewrite the term with the negative exponent as a fraction. (dy)/(dx) = 2e^x + (3)/(x) - (2)/(x^3) The final answer is 2e^x + (3)/(x) - (2)/(x^3). 3 done, 2 left today. You're making progress.