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

The derivative of (x^2-1(-3x^3+2x)) is -15x^4+15x^2-2

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

The first derivative of (x^2-1(-3x^3+2x)) is -15x^4+15x^2-2

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\frac{d}{d x} ((x^{2} - 1) (- 3 x^{3} + 2 x))

- 15 x^{4} + 15 x^{2} - 2

Solution steps

\frac{d}{d x} ((x^{2} - 1) (- 3 x^{3} + 2 x))

Apply the Product Rule:

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

f = x^{2} - 1, g = - 3 x^{3} + 2 x

= \frac{d}{d x} (x^{2} - 1) (- 3 x^{3} + 2 x) + \frac{d}{d x} (- 3 x^{3} + 2 x) (x^{2} - 1)

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

\frac{d}{d x} (- 3 x^{3} + 2 x) = - 9 x^{2} + 2

= 2 x (- 3 x^{3} + 2 x) + (- 9 x^{2} + 2) (x^{2} - 1)

Simplify

2 x (- 3 x^{3} + 2 x) + (- 9 x^{2} + 2) (x^{2} - 1) : - 15 x^{4} + 15 x^{2} - 2

= - 15 x^{4} + 15 x^{2} - 2

What is the derivative of (x^2-1(-3x^3+2x)) ?
The derivative of (x^2-1(-3x^3+2x)) is -15x^4+15x^2-2
What is the first derivative of (x^2-1(-3x^3+2x)) ?
The first derivative of (x^2-1(-3x^3+2x)) is -15x^4+15x^2-2