Calculus Examples

$f (x) = 50 - 2 \sqrt{400}$

Step 1

Differentiate.

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Step 1.1

Rewrite $400$ as $20^{2}$ .

$\frac{d}{d x} [50 - 2 \sqrt{20^{2}}]$

Step 1.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{d}{d x} [50 - 2 \cdot 20]$

Step 1.3

By the Sum Rule, the derivative of $50 - 2 \cdot 20$ with respect to $x$ is $\frac{d}{d x} [50] + \frac{d}{d x} [- 2 \cdot 20]$ .

$\frac{d}{d x} [50] + \frac{d}{d x} [- 2 \cdot 20]$

Step 1.4

Since $50$ is constant with respect to $x$ , the derivative of $50$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [- 2 \cdot 20]$

Step 2

Evaluate $\frac{d}{d x} [- 2 \cdot 20]$ .

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Step 2.1

Multiply $- 2$ by $20$ .

$0 + \frac{d}{d x} [- 40]$

Step 2.2

Since $- 40$ is constant with respect to $x$ , the derivative of $- 40$ with respect to $x$ is $0$ .

$0 + 0$

Step 3

Add $0$ and $0$ .

$0$