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

The derivative of (x^3+1(3-2x^3)) is -12x^5+3x^2

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

The first derivative of (x^3+1(3-2x^3)) is -12x^5+3x^2

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

- 12 x^{5} + 3 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

3 x^{2} (3 - 2 x^{3}) + (- 6 x^{2}) (x^{3} + 1) : - 12 x^{5} + 3 x^{2}

= - 12 x^{5} + 3 x^{2}

What is the derivative of (x^3+1(3-2x^3)) ?
The derivative of (x^3+1(3-2x^3)) is -12x^5+3x^2
What is the first derivative of (x^3+1(3-2x^3)) ?
The first derivative of (x^3+1(3-2x^3)) is -12x^5+3x^2