# How do you differentiate #g(y) =x(x^2 - 1) # using the product rule?

##### 1 Answer

Mar 4, 2017

#### Answer:

# (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 #