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

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

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

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

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

4 - 3 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot (4 - x^{2}) + (- 2 x) x : 4 - 3 x^{2}

= 4 - 3 x^{2}

- x \frac{d y}{d x} = x^{2} - y

x \to 0 lim (\frac{3}{x ( 2 \cdot x + 1 )})

\frac{\partial}{\partial x} (x^{3} + y^{3} - 6 x y)

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

n = 0 \sum \infty n

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