Calculus Examples

$f (x) = 15000 + 70 (100) + \frac{1000}{100}$

Step 1

Differentiate.

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Step 1.1

Divide $1000$ by $100$ .

$\frac{d}{d x} [15000 + 70 (100) + 10]$

Step 1.2

By the Sum Rule, the derivative of $15000 + 70 (100) + 10$ with respect to $x$ is $\frac{d}{d x} [15000] + \frac{d}{d x} [70 (100)] + \frac{d}{d x} [10]$ .

$\frac{d}{d x} [15000] + \frac{d}{d x} [70 (100)] + \frac{d}{d x} [10]$

Step 1.3

Since $15000$ is constant with respect to $x$ , the derivative of $15000$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [70 (100)] + \frac{d}{d x} [10]$

Step 2

Evaluate $\frac{d}{d x} [70 (100)]$ .

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Step 2.1

Multiply $70$ by $100$ .

$0 + \frac{d}{d x} [7000] + \frac{d}{d x} [10]$

Step 2.2

Since $7000$ is constant with respect to $x$ , the derivative of $7000$ with respect to $x$ is $0$ .

$0 + 0 + \frac{d}{d x} [10]$

Step 3

Since $10$ is constant with respect to $x$ , the derivative of $10$ with respect to $x$ is $0$ .

$0 + 0 + 0$

Step 4

Combine terms.

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Step 4.1

Add $0$ and $0$ .

$0 + 0$

Step 4.2

Add $0$ and $0$ .

$0$