What is the derivative of (x^2-1(-x^2-4x-2)) ?

The derivative of (x^2-1(-x^2-4x-2)) is -4x^3-12x^2-2x+4

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

The first derivative of (x^2-1(-x^2-4x-2)) is -4x^3-12x^2-2x+4

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\frac{d}{d x} ((x^{2} - 1) (- x^{2} - 4 x - 2))

- 4 x^{3} - 12 x^{2} - 2 x + 4

Solution steps

\frac{d}{d x} ((x^{2} - 1) (- x^{2} - 4 x - 2))

Apply the Product Rule:

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

f = x^{2} - 1, g = - x^{2} - 4 x - 2

= \frac{d}{d x} (x^{2} - 1) (- x^{2} - 4 x - 2) + \frac{d}{d x} (- x^{2} - 4 x - 2) (x^{2} - 1)

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

\frac{d}{d x} (- x^{2} - 4 x - 2) = - 2 x - 4

= 2 x (- x^{2} - 4 x - 2) + (- 2 x - 4) (x^{2} - 1)

Simplify

2 x (- x^{2} - 4 x - 2) + (- 2 x - 4) (x^{2} - 1) : - 4 x^{3} - 12 x^{2} - 2 x + 4

= - 4 x^{3} - 12 x^{2} - 2 x + 4

\frac{\partial}{\partial x} (5 x^{2} y^{5})

\frac{\partial}{\partial y} (x y^{6} + x^{2} + y^{4})

\frac{\partial}{\partial z} (arctan (\frac{x}{z}))

- 2 x^{2} + 50 x + 25.247

\frac{d}{d x} (x^{3} + 10)

What is the derivative of (x^2-1(-x^2-4x-2)) ?
The derivative of (x^2-1(-x^2-4x-2)) is -4x^3-12x^2-2x+4
What is the first derivative of (x^2-1(-x^2-4x-2)) ?
The first derivative of (x^2-1(-x^2-4x-2)) is -4x^3-12x^2-2x+4