Find the indicated derivative in each case. Simplify your answers completely which means reduced fraction to lowest terms, no compound fractions, complete factor form and no negative exponents. Question 9 does not need a common denominator since there are 4 different terms given. DO the quotient rule on problems 1, 2, 10, 17, and 18. Problem 8 is a piecewise function. There is not sufficient amount of room on this sheet to do the work required. Show your work on another piece of paper and write your simplified answer below. Attach your work. 1. f'(t) for f (t) = VP + 1 2. f' ( x) for f ( x) = * +1 x3 3. " for z = (x + 1)' (5 -x)* dx 4. f'(m) for f(m) =- 1 sec(2m) 5. f"(x) for f(x) = 3x- 25x 6. f'(f) for f(D) = PT +r 1 - B 7. dy for y = In(In(2t')) dt 8. g'(x) for g(x) = x.e (write g as a piecewise function, then find the derivative of the function) 9. x'(r) for x (r) = 3r +3Vr-3+ 53 10. h'(y) for h(y) = In y 1-In y11. dz for z = log(102m ) dm 12. f (x) for f(x) = cos*(m . 2x) 13. f'(t) for f(t) = sin-' =) 14. g'(0) for g(0) = 30 + tan (40) 15. f'(x) for f(x) = xcos(x+1) 16. " dy for y = (cot 1 + cotu)" du e az 17. g'(z) for g(z) =- a + z z 18. f'(x) for f (x) =- (2-x) 3 19. a'(t) and a"(t) for a(t) = In 1-cost + (1+ cost (Simplify a'(t) completely before taking the second derivative. Both need to be simplified completely) 20. L'(D) for L(D) = arctan ()