y′ = x^5 (tan x)′ + (x^5 )′ (tan x).(A) By the Quotient Rule, (6),(B) Since y = (3 − 2x)1/2, by the Power Rule, (3),(B) Since y = 2(5x + 1)−^3 , y′ = −6(5x + 1)−^4 (5).(E)(D) Rewrite: (A) Rewrite: y = (x^2 + 2x − 1)1/2 ; then y = (x^2 + 2x − 1)−1/2(2x + 2).(D) Use the Quotient Rule:(C) Since
y = ln ex − ln(ex − 1)