Calculus Examples

$y = 7 - x^{2}$ , $x = - 2$

Step 1

Differentiate.

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Step 1.1

By the Sum Rule, the derivative of $7 - x^{2}$ with respect to $x$ is $\frac{d}{d x} [7] + \frac{d}{d x} [- x^{2}]$ .

$\frac{d}{d x} [7] + \frac{d}{d x} [- x^{2}]$

Step 1.2

Since $7$ is constant with respect to $x$ , the derivative of $7$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [- x^{2}]$

Step 2

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

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Step 2.1

Since $- 1$ is constant with respect to $x$ , the derivative of $- x^{2}$ with respect to $x$ is $- \frac{d}{d x} [x^{2}]$ .

$0 - \frac{d}{d x} [x^{2}]$

Step 2.2

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

$0 - (2 x)$

Step 2.3

Multiply $2$ by $- 1$ .

$0 - 2 x$

Step 3

Subtract $2 x$ from $0$ .

$- 2 x$

Step 4

Evaluate the derivative at $x = - 2$ .

$- 2 \cdot - 2$

Step 5

Multiply $- 2$ by $- 2$ .

$4$