Calculus Examples

$y = 5 (3 - x)$ , $x = 1$

Step 1

Since $5$ is constant with respect to $x$ , the derivative of $5 (3 - x)$ with respect to $x$ is $5 \frac{d}{d x} [3 - x]$ .

$5 \frac{d}{d x} [3 - x]$

Step 2

By the Sum Rule, the derivative of $3 - x$ with respect to $x$ is $\frac{d}{d x} [3] + \frac{d}{d x} [- x]$ .

$5 (\frac{d}{d x} [3] + \frac{d}{d x} [- x])$

Step 3

Since $3$ is constant with respect to $x$ , the derivative of $3$ with respect to $x$ is $0$ .

$5 (0 + \frac{d}{d x} [- x])$

Step 4

Add $0$ and $\frac{d}{d x} [- x]$ .

$5 \frac{d}{d x} [- x]$

Step 5

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

$5 (- \frac{d}{d x} [x])$

Step 6

Multiply $- 1$ by $5$ .

$- 5 \frac{d}{d x} [x]$

Step 7

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

$- 5 \cdot 1$

Step 8

Multiply $- 5$ by $1$ .

$- 5$

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