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

The derivative of f(x)=x^2(-3x^2-2) is -12x^3-4x

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

The first derivative of f(x)=x^2(-3x^2-2) is -12x^3-4x

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derivative of

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

- 12 x^{3} - 4 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= - 12 x^{3} - 4 x

What is the derivative of f(x)=x^2(-3x^2-2) ?
The derivative of f(x)=x^2(-3x^2-2) is -12x^3-4x
What is the first derivative of f(x)=x^2(-3x^2-2) ?
The first derivative of f(x)=x^2(-3x^2-2) is -12x^3-4x