Question 7

a function of x, and assume x and y are positive. Find y' if xy =y". 7. Let f(x) = In(x - 1). Find the first, second, third, fourth and n-th derivative of f. As well, use mathematical induction to prove the n-th derivative of f is correct. As part of your solution, briefly explain what is mathematical induction. Hint: recall the definition of factorial is r! = 1 . 2 . 3 ...(r - 1) . ..r where r is a non-negative integer, and by convention 0! = 1. 8. Find and explain the error in the following: 2-2+1 2 2 dx =