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

The derivative of x(4-x^2^2) is 5x^4-24x^2+16

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

The first derivative of x(4-x^2^2) is 5x^4-24x^2+16

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

5 x^{4} - 24 x^{2} + 16

Solution steps

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

Apply the Product Rule:

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

f = x, g = (4 - x^{2})^{2}

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

\frac{d x}{d x} = 1

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

= 1 \cdot (4 - x^{2})^{2} + (- 4 x (4 - x^{2})) x

Simplify

1 \cdot (4 - x^{2})^{2} + (- 4 x (4 - x^{2})) x : 5 x^{4} - 24 x^{2} + 16

= 5 x^{4} - 24 x^{2} + 16

What is the derivative of x(4-x^2^2) ?
The derivative of x(4-x^2^2) is 5x^4-24x^2+16
What is the first derivative of x(4-x^2^2) ?
The first derivative of x(4-x^2^2) is 5x^4-24x^2+16