Calculus Examples

$f (x) = 5 {(10 - 2)}^{2} - 2 (10 - 2) + 6$

Step 1

Differentiate using the Sum Rule.

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Step 1.1

Subtract $2$ from $10$ .

$\frac{d}{d x} [5 \cdot 8^{2} - 2 (10 - 2) + 6]$

Step 1.2

Simplify the expression.

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Step 1.2.1

Raise $8$ to the power of $2$ .

$\frac{d}{d x} [5 \cdot 64 - 2 (10 - 2) + 6]$

Step 1.2.2

Subtract $2$ from $10$ .

$\frac{d}{d x} [5 \cdot 64 - 2 \cdot 8 + 6]$

Step 1.3

By the Sum Rule, the derivative of $5 \cdot 64 - 2 \cdot 8 + 6$ with respect to $x$ is $\frac{d}{d x} [5 \cdot 64] + \frac{d}{d x} [- 2 \cdot 8] + \frac{d}{d x} [6]$ .

$\frac{d}{d x} [5 \cdot 64] + \frac{d}{d x} [- 2 \cdot 8] + \frac{d}{d x} [6]$

Step 2

Evaluate $\frac{d}{d x} [5 \cdot 64]$ .

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Step 2.1

Multiply $5$ by $64$ .

$\frac{d}{d x} [320] + \frac{d}{d x} [- 2 \cdot 8] + \frac{d}{d x} [6]$

Step 2.2

Since $320$ is constant with respect to $x$ , the derivative of $320$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [- 2 \cdot 8] + \frac{d}{d x} [6]$

Step 3

Evaluate $\frac{d}{d x} [- 2 \cdot 8]$ .

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Step 3.1

Multiply $- 2$ by $8$ .

$0 + \frac{d}{d x} [- 16] + \frac{d}{d x} [6]$

Step 3.2

Since $- 16$ is constant with respect to $x$ , the derivative of $- 16$ with respect to $x$ is $0$ .

$0 + 0 + \frac{d}{d x} [6]$

Step 4

Since $6$ is constant with respect to $x$ , the derivative of $6$ with respect to $x$ 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 $0$ .

$0$