find the derivative of y 9e6x 5x3Solution Explanation Use q

Solution

?Explanation? Use quotient rule to take a derivative of that function. Know that quotient rule is: F(x) = f(x)/g(x) F\'(x) = [g(x)f\'(x) - f(x)g\'(x)]/[g²(x)] Let: f(x) = -9e^(6x) g(x) = 5x + 3 f\'(x) = -54e^(6x) [because of y = e^f(x) ? y\' = f\'(x)*e^f(x)] g\'(x) = 5 Substitute those to the formula and rewrite the new equation and simplify. [(5x + 3)(-54e^(6x)) - (9e^(6x))(5)]/(5x + 3)² Therefore, you get: (-9e^(6x))(30x + 13)/(5x + 3)²