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

The derivative of (x^2-1(x^3+3x)) is 5x^4+6x^2-3

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

The first derivative of (x^2-1(x^3+3x)) is 5x^4+6x^2-3

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

5 x^{4} + 6 x^{2} - 3

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x (x^{3} + 3 x) + (3 x^{2} + 3) (x^{2} - 1) : 5 x^{4} + 6 x^{2} - 3

= 5 x^{4} + 6 x^{2} - 3

What is the derivative of (x^2-1(x^3+3x)) ?
The derivative of (x^2-1(x^3+3x)) is 5x^4+6x^2-3
What is the first derivative of (x^2-1(x^3+3x)) ?
The first derivative of (x^2-1(x^3+3x)) is 5x^4+6x^2-3