Precalculus Examples

$(f - g) (- 3)$

Step 1

Move $- 3$ to the left of $f - g$ .

$\frac{d}{d f} [- 3 \cdot (f - g)]$

Step 2

Since $- 3$ is constant with respect to $f$ , the derivative of $- 3 (f - g)$ with respect to $f$ is $- 3 \frac{d}{d f} [f - g]$ .

$- 3 \frac{d}{d f} [f - g]$

Step 3

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

$- 3 (\frac{d}{d f} [f] + \frac{d}{d f} [- g])$

Step 4

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

$- 3 (1 + \frac{d}{d f} [- g])$

Step 5

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

$- 3 (1 + 0)$

Step 6

Simplify the expression.

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Step 6.1

Add $1$ and $0$ .

$- 3 \cdot 1$

Step 6.2

Multiply $- 3$ by $1$ .

$- 3$