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

The derivative of (x^2-3)(x^3-2x) is 5x^4-15x^2+6

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

The first derivative of (x^2-3)(x^3-2x) is 5x^4-15x^2+6

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derivative of

(x^{2} - 3) (x^{3} - 2 x)

5 x^{4} - 15 x^{2} + 6

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x (x^{3} - 2 x) + (3 x^{2} - 2) (x^{2} - 3) : 5 x^{4} - 15 x^{2} + 6

= 5 x^{4} - 15 x^{2} + 6

\int_{3}^{9} 1 + x^{4} + 2 x^{2} d x

\int (b - x)^{2} d x

\frac{d}{d x} (18 x^{2})

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

What is the derivative of (x^2-3)(x^3-2x) ?
The derivative of (x^2-3)(x^3-2x) is 5x^4-15x^2+6
What is the first derivative of (x^2-3)(x^3-2x) ?
The first derivative of (x^2-3)(x^3-2x) is 5x^4-15x^2+6