Calculus Examples

$f (x) - f \cdot 2$

Step 1

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

$\frac{d}{d x} [f (x)] + \frac{d}{d x} [- f \cdot 2]$

Step 2

Differentiate using the function rule which states that the derivative of $f (x)$ is $\frac{d f}{d x}$ .

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

Step 3

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

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Step 3.1

Multiply $2$ by $- 1$ .

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

Step 3.2

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

$\frac{d f}{d x} + 0$

Step 4

Add $\frac{d f}{d x}$ and $0$ .

$\frac{d f}{d x}$