Calculus Examples

$a \cdot 1 = 6 n$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d n} (a \cdot 1) = \frac{d}{d n} (6 n)$

Step 2

Differentiate the left side of the equation.

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Step 2.1

Multiply $a$ by $1$ .

$\frac{d}{d n} [a]$

Step 2.2

Rewrite $\frac{d}{d n} [a]$ as $a'$ .

$a'$

Step 3

Differentiate the right side of the equation.

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Step 3.1

Since $6$ is constant with respect to $n$ , the derivative of $6 n$ with respect to $n$ is $6 \frac{d}{d n} [n]$ .

$6 \frac{d}{d n} [n]$

Step 3.2

Differentiate using the Power Rule which states that $\frac{d}{d n} [n^{n}]$ is $n \cdot n^{n - 1}$ where $n = 1$ .

$6 \cdot 1$

Step 3.3

Multiply $6$ by $1$ .

$6$

Step 4

Reform the equation by setting the left side equal to the right side.

$a' = 6$

Step 5

Replace $a'$ with $\frac{d a}{d n}$ .

$\frac{d a}{d n} = 6$