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)