What is the derivative of 1000(1-x/(500)^2) ?

The derivative of 1000(1-x/(500)^2) is -4(1-x/(500))

What is the first derivative of 1000(1-x/(500)^2) ?

The first derivative of 1000(1-x/(500)^2) is -4(1-x/(500))

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\frac{d}{d x} (1000 (1 - \frac{x}{500})^{2})

- 4 (1 - \frac{x}{500})

Solution steps

\frac{d}{d x} (1000 (1 - \frac{x}{500})^{2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 1000 \frac{d}{d x} ((1 - \frac{x}{500})^{2})

Apply the chain rule:

2 (1 - \frac{x}{500}) \frac{d}{d x} (1 - \frac{x}{500})

= 2 (1 - \frac{x}{500}) \frac{d}{d x} (1 - \frac{x}{500})

\frac{d}{d x} (1 - \frac{x}{500}) = - \frac{1}{500}

= 1000 \cdot 2 (1 - \frac{x}{500}) (- \frac{1}{500})

Simplify

1000 \cdot 2 (1 - \frac{x}{500}) (- \frac{1}{500}) : - 4 (1 - \frac{x}{500})

= - 4 (1 - \frac{x}{500})

What is the derivative of 1000(1-x/(500)^2) ?
The derivative of 1000(1-x/(500)^2) is -4(1-x/(500))
What is the first derivative of 1000(1-x/(500)^2) ?
The first derivative of 1000(1-x/(500)^2) is -4(1-x/(500))