Calculus Examples

$f (x) = 16 ({3.5}^{2}) + 112 (3.5) + 70$

Step 1

Differentiate using the Sum Rule.

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Step 1.1

Raise $3.5$ to the power of $2$ .

$\frac{d}{d x} [16 \cdot 12.25 + 112 (3.5) + 70]$

Step 1.2

By the Sum Rule, the derivative of $16 \cdot 12.25 + 112 (3.5) + 70$ with respect to $x$ is $\frac{d}{d x} [16 \cdot 12.25] + \frac{d}{d x} [112 (3.5)] + \frac{d}{d x} [70]$ .

$\frac{d}{d x} [16 \cdot 12.25] + \frac{d}{d x} [112 (3.5)] + \frac{d}{d x} [70]$

Step 2

Evaluate $\frac{d}{d x} [16 \cdot 12.25]$ .

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Step 2.1

Multiply $16$ by $12.25$ .

$\frac{d}{d x} [196] + \frac{d}{d x} [112 (3.5)] + \frac{d}{d x} [70]$

Step 2.2

Since $196$ is constant with respect to $x$ , the derivative of $196$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [112 (3.5)] + \frac{d}{d x} [70]$

Step 3

Evaluate $\frac{d}{d x} [112 (3.5)]$ .

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Step 3.1

Multiply $112$ by $3.5$ .

$0 + \frac{d}{d x} [392] + \frac{d}{d x} [70]$

Step 3.2

Since $392$ is constant with respect to $x$ , the derivative of $392$ with respect to $x$ is $0$ .

$0 + 0 + \frac{d}{d x} [70]$

Step 4

Since $70$ is constant with respect to $x$ , the derivative of $70$ 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 $0$ .

$0$