What is (\partial)/(\partial x)((x^2-a-1)(x^2+a-1)) ?

The answer to (\partial)/(\partial x)((x^2-a-1)(x^2+a-1)) is 4x^3-4x

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(\partial)/(\partial x)((x^2-a-1)(x^2+a-1))

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

4 x^{3} - 4 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 4 x^{3} - 4 x

\frac{\partial}{\partial x} (3 x^{2} + y^{2})

y = 3 x^{2} + e^{2} x + π^{2}

y = (1 + 4 (2))^{\frac{3}{2}}

\int_{0}^{x} 36 - t^{2} d t

\frac{d}{d x} ((2 x^{5} - 3)^{8})

What is (\partial)/(\partial x)((x^2-a-1)(x^2+a-1)) ?
The answer to (\partial)/(\partial x)((x^2-a-1)(x^2+a-1)) is 4x^3-4x