Question

10 POINTS!!! FULL ANSWER WITH FULL STEP BY STEP SOLUTION PLEASE. DO BOTH PARTS OF 3 AND ALL OF 4.

Answer 1

3. Recognize that log(x) = ln(x)/ln(10)

3a) (d/dx)(ln(x)/(ln(x)/ln(10)) = (d/dx)(ln(10)) = 0

3b) (d/dx)(ln(log(x)) = (d/dx)(ln(ln(x)/ln(10))) = (d/dx)(ln(ln(x)) -ln(1/ln(10)))
.. = (d/dx)(ln(ln(x))) . . . . . . . . simplified form
.. = (1/ln(x))*(d/dx)(ln(x))
.. = 1/(x*ln(x))


4. y' = 1/x
.. y'' = -1/x^2
.. y''' = 2/x^3
.. yⁿ = -(n-1)!*(-1/x)ⁿ

Answer 2

see the attached picture for the answers: