Calculus Examples

$y = x^{2} - 2 x$ , $x = - 3$

Step 1

Differentiate.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

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Step 2.1

Since $- 2$ is constant with respect to $x$ , the derivative of $- 2 x$ with respect to $x$ is $- 2 \frac{d}{d x} [x]$ .

$2 x - 2 \frac{d}{d x} [x]$

Step 2.2

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

$2 x - 2 \cdot 1$

Step 2.3

Multiply $- 2$ by $1$ .

$2 x - 2$

Step 3

Evaluate the derivative at $x = - 3$ .

$2 (- 3) - 2$

Step 4

Simplify.

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Step 4.1

Multiply $2$ by $- 3$ .

$- 6 - 2$

Step 4.2

Subtract $2$ from $- 6$ .

$- 8$

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