What is the derivative of x^3(4-x^2) ?

The derivative of x^3(4-x^2) is 12x^2-5x^4

What is the first derivative of x^3(4-x^2) ?

The first derivative of x^3(4-x^2) is 12x^2-5x^4

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\frac{d}{d x} (x^{3} (4 - x^{2}))

12 x^{2} - 5 x^{4}

Solution steps

\frac{d}{d x} (x^{3} (4 - x^{2}))

Apply the Product Rule:

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

f = x^{3}, g = 4 - x^{2}

= \frac{d}{d x} (x^{3}) (4 - x^{2}) + \frac{d}{d x} (4 - x^{2}) x^{3}

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

\frac{d}{d x} (4 - x^{2}) = - 2 x

= 3 x^{2} (4 - x^{2}) + (- 2 x) x^{3}

Simplify

3 x^{2} (4 - x^{2}) + (- 2 x) x^{3} : 12 x^{2} - 5 x^{4}

= 12 x^{2} - 5 x^{4}

What is the derivative of x^3(4-x^2) ?
The derivative of x^3(4-x^2) is 12x^2-5x^4
What is the first derivative of x^3(4-x^2) ?
The first derivative of x^3(4-x^2) is 12x^2-5x^4