Find the derivative of fxe6xx26x fxSolution Given fx e6x x2

Solution

Given: f(x) = e^6x (x^2 + 6^x) Note: d/dx e^6x = 6e^6x and: d/dx (x^2+6^x) = 2x + 6^x*ln(6) So, taking the derivative using the product rule: f\'(x) = e^6x * [2x + 6^x*ln(6)] + (x^2+6^x) * 6e^6x Obviously this could be rearranged algebraically since both terms contain e^6x, but\'s it is probably sufficient as it stands above. Alternatively, it could be rewritten as: f\'(x) = e^6x * [2x + 6^x*ln(6) + 6(x^2+6^x)] f\'(x) = e^6x * [2x + 6^x*ln(6) + 6x^2 + 6*6^x] f\'(x) = e^6x * [2x + 6^x*ln(6) + 6x^2 + 6^(x+1)]