How do you differentiate #g(y) =x(x^2 - 1) # using the product rule?
1 Answer
Mar 4, 2017
# (dg)/dx = 3x^2 -1 #
Explanation:
Although we can use the product rule, it is easier to multiply out:
Method 1 - Product Rule
# (dg)/dx = (x)(d/dx (x^2-1) ) + (d/dx x)(x^2-1) #
# \ \ \ \ \ \ = (x)(2x ) + (1)(x^2-1) #
# \ \ \ \ \ \ = 2x^2 + x^2 -1 #
# \ \ \ \ \ \ = 3x^2 -1 #
Method 2 - Multiply Out
# g(y) = x^3-x #
# (dg)/dx = 3x^2 -1 #
