What is the derivative of (x^2+1(x^2-1)) ?

The derivative of (x^2+1(x^2-1)) is 4x^3

What is the first derivative of (x^2+1(x^2-1)) ?

The first derivative of (x^2+1(x^2-1)) is 4x^3

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\frac{d}{d x} ((x^{2} + 1) (x^{2} - 1))

4 x^{3}

Solution steps

\frac{d}{d x} ((x^{2} + 1) (x^{2} - 1))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2} + 1, g = x^{2} - 1

= \frac{d}{d x} (x^{2} + 1) (x^{2} - 1) + \frac{d}{d x} (x^{2} - 1) (x^{2} + 1)

\frac{d}{d x} (x^{2} + 1) = 2 x

\frac{d}{d x} (x^{2} - 1) = 2 x

= 2 x (x^{2} - 1) + 2 x (x^{2} + 1)

Simplify

2 x (x^{2} - 1) + 2 x (x^{2} + 1) : 4 x^{3}

= 4 x^{3}

What is the derivative of (x^2+1(x^2-1)) ?
The derivative of (x^2+1(x^2-1)) is 4x^3
What is the first derivative of (x^2+1(x^2-1)) ?
The first derivative of (x^2+1(x^2-1)) is 4x^3