Question

WebWorkTutorial: Problem 6 Previous Problem Problem List Next Problem (1 point) This page contains revision on differentiation and integration techniques Question 8. Suppose that f(x)- 6e-5x log(x). Find f'(3). f'(3) Question 9. Letf(x) = x4 arctan(2x). Find,f,(x) f x) Question 10. Differentiate

Answer 1

f(x) = 6 e^-5x log x using (d/dx (u, v) = u du/dx + u dv/dx) here u = e^-sx v = log x d f(x)/dx = d/dx (6e^-sx log x) = 6 log x d/dx e^_sx + 6 e^-sx d/dx log x = 6 log x(-se^-sx) +^e^-sx 1 f'(x) = 6 e^-sx (-5 logx + 1/x) at x = 3 f'(3) = 6 e^-1s (-s log 3 + 1/3) f'(3) = 2 e^-1s (-1s log 3 + 1) \r\n f(x) = x^4 tan^-1 (2x) using d/dx (u v) = v du/dx + u du/dx here u = x^4 v = tan^-1 (2x) d f(x)/dx = d/dx (x^4 tan^-1(2x)) = tan^-1(2x) dx^2/dx + x^4 d/dx tan^-1 2x = tan^-1(2x) 4x^3 + x^4 (2/1 + (2x)^2) = 4x^3 tan^-1 2x + 2x^4/1 + 4x^2 f'(x) = 2x^3 (2 tan^-1 2x + x/1 + 4x^2)