Calculus Examples

$X^{2} + 2 x + 1$

Step 1

By the Sum Rule, the derivative of $X^{2} + 2 x + 1$ with respect to $X$ is $\frac{d}{d X} [X^{2}] + \frac{d}{d X} [2 x] + \frac{d}{d X} [1]$ .

$\frac{d}{d X} [X^{2}] + \frac{d}{d X} [2 x] + \frac{d}{d X} [1]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d X} [X^{n}]$ is $n X^{n - 1}$ where $n = 2$ .

$2 X + \frac{d}{d X} [2 x] + \frac{d}{d X} [1]$

Step 3

Since $2 x$ is constant with respect to $X$ , the derivative of $2 x$ with respect to $X$ is $0$ .

$2 X + 0 + \frac{d}{d X} [1]$

Step 4

Since $1$ is constant with respect to $X$ , the derivative of $1$ with respect to $X$ is $0$ .

$2 X + 0 + 0$

Step 5

Combine terms.

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Step 5.1

Add $2 X$ and $0$ .

$2 X + 0$

Step 5.2

Add $2 X$ and $0$ .

$2 X$