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

The derivative of (3x^2-3x+1)(x^3) is 15x^4-12x^3+3x^2

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

The first derivative of (3x^2-3x+1)(x^3) is 15x^4-12x^3+3x^2

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (3 x^{2} - 3 x + 1) = 6 x - 3

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

= (6 x - 3) x^{3} + 3 x^{2} (3 x^{2} - 3 x + 1)

Simplify

(6 x - 3) x^{3} + 3 x^{2} (3 x^{2} - 3 x + 1) : 15 x^{4} - 12 x^{3} + 3 x^{2}

= 15 x^{4} - 12 x^{3} + 3 x^{2}

What is the derivative of (3x^2-3x+1)(x^3) ?
The derivative of (3x^2-3x+1)(x^3) is 15x^4-12x^3+3x^2
What is the first derivative of (3x^2-3x+1)(x^3) ?
The first derivative of (3x^2-3x+1)(x^3) is 15x^4-12x^3+3x^2