What is the first derivative and second derivative of x^4 - 1?

1 Answer
May 31, 2016

f^'(x)=4x^3
f^''(x)=12x^2

Explanation:

to find the first derivative we must simply use three rules:

1. Power rule
d/dx x^n = nx^(n-1)

2. Constant rule
d/dx (c) = 0 (where c is an integer and not a variable)

3. Sum and difference rule
d/dx [f(x)+-g(x)] = [f^'(x)+-g^'(x)]

the first derivative results in:
4x^3-0
which simplifies to
4x^3

to find the second derivative, we must derive the first derivative by again applying the power rule which results in:
12x^3

you can keep going if you like:
third derivative = 36x^2
fourth derivative = 72x
fifth derivative = 72
sixth derivative = 0