# What is the second derivative of? : #2(x^2-1)^3#

##### 2 Answers

#### Explanation:

To find the second derivative, you need to find the first derivative, so let's do that immediately:

I used the chain rule and product rule to find the first derivative. Now let's find the second derivative:

For the second derivative, I used the product rule and chain rule.

# (d^2)/(dx^2) 2(x^2-1)^3 = 12(x^2-1)(5x^2-1) #

#### Explanation:

First we generate the first derivative using the chain rule:

# d/dx 2(x^2-1)^3 = 2(3)2(x^2-1)^2 d/dx ( x^2-1)#

# " " = 6(x^2-1)^2 (2x)#

# " " = 12x(x^2-1)^2#

Then, we generate the second derivative using the product rule and the chain rule:

# (d^2)/(dx^2) 2(x^2-1)^3 = d/dx 12x(x^2-1)^2 #

# " " = 12x(d/dx (x^2-1)^2) + (d/dx12x)(x^2-1)^2 #

# " " = 12x(2(x^2-1)(d/dx(x^2-1))) + 12(x^2-1)^2 #

# " " = 24x(x^2-1)(2x) + 12(x^2-1)^2 #

# " " = 12(x^2-1){4x^2 + (x^2-1)} #

# " " = 12(x^2-1)(5x^2-1) #