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

Answer 1

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

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#
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Answer 2

The first derivative of (x^4 - 1) is (4x^3).

The second derivative of (x^4 - 1) is (12x^2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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