Basic Rules

Question 1

y = f(x)g(x)

Answer 1

y’ = f’(x)g(x) + g’(x)f(x)

Question 2

y = f(x) / g(x)

Answer 2

y’ = f’(x) g(x) + g’(x) f(x)/ (g(x))^2

Question 3

y = (f(g(x))

Answer 3

y’ = g’(x) f’(g(x))

Question 4

y = (f(g(h(x))))

Answer 4

y’ = h’(x) g’h(x) f’(g(h(x)))

Question 5

y = c

Answer 5

y’ = 0

Question 6

y = x^n, y = u^n

Answer 6

y’ = n x^n-1, y’ = n u’ u^n-1

Question 7

y = 1/x

Answer 7

y’ = -1/x^2

Question 8

y = sqrt(x), y = sqrt(u)

Answer 8

y’ = 1/2sqrt(x), y’ = u’/2sqrt(u)