Calculus Examples

$a = 12 x + \frac{192}{x} + 96$

Step 1

By the Sum Rule, the derivative of $12 x + \frac{192}{x} + 96$ with respect to $a$ is $\frac{d}{d a} [12 x] + \frac{d}{d a} [\frac{192}{x}] + \frac{d}{d a} [96]$ .

$\frac{d}{d a} [12 x] + \frac{d}{d a} [\frac{192}{x}] + \frac{d}{d a} [96]$

Step 2

Since $12 x$ is constant with respect to $a$ , the derivative of $12 x$ with respect to $a$ is $0$ .

$0 + \frac{d}{d a} [\frac{192}{x}] + \frac{d}{d a} [96]$

Step 3

Since $\frac{192}{x}$ is constant with respect to $a$ , the derivative of $\frac{192}{x}$ with respect to $a$ is $0$ .

$0 + 0 + \frac{d}{d a} [96]$

Step 4

Since $96$ is constant with respect to $a$ , the derivative of $96$ with respect to $a$ is $0$ .

$0 + 0 + 0$

Step 5

Combine terms.

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Step 5.1

Add $0$ and $0$ .

$0 + 0$

Step 5.2

Add $0$ and $0$ .

$0$