Calculus Examples

$1200 + 12 x - 0.1 x^{2} + 0 x^{3}$

Step 1

Differentiate.

Tap for more steps...

Step 1.1

By the Sum Rule, the derivative of $1200 + 12 x - 0.1 x^{2} + 0 x^{3}$ with respect to $x$ is $\frac{d}{d x} [1200] + \frac{d}{d x} [12 x] + \frac{d}{d x} [- 0.1 x^{2}] + \frac{d}{d x} [0 x^{3}]$ .

$\frac{d}{d x} [1200] + \frac{d}{d x} [12 x] + \frac{d}{d x} [- 0.1 x^{2}] + \frac{d}{d x} [0 x^{3}]$

Step 1.2

Since $1200$ is constant with respect to $x$ , the derivative of $1200$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [12 x] + \frac{d}{d x} [- 0.1 x^{2}] + \frac{d}{d x} [0 x^{3}]$

Step 2

Evaluate $\frac{d}{d x} [12 x]$ .

Tap for more steps...

Step 2.1

Since $12$ is constant with respect to $x$ , the derivative of $12 x$ with respect to $x$ is $12 \frac{d}{d x} [x]$ .

$0 + 12 \frac{d}{d x} [x] + \frac{d}{d x} [- 0.1 x^{2}] + \frac{d}{d x} [0 x^{3}]$

Step 2.2

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

$0 + 12 \cdot 1 + \frac{d}{d x} [- 0.1 x^{2}] + \frac{d}{d x} [0 x^{3}]$

Step 2.3

Multiply $12$ by $1$ .

$0 + 12 + \frac{d}{d x} [- 0.1 x^{2}] + \frac{d}{d x} [0 x^{3}]$

Step 3

Evaluate $\frac{d}{d x} [- 0.1 x^{2}]$ .

Tap for more steps...

Step 3.1

Since $- 0.1$ is constant with respect to $x$ , the derivative of $- 0.1 x^{2}$ with respect to $x$ is $- 0.1 \frac{d}{d x} [x^{2}]$ .

$0 + 12 - 0.1 \frac{d}{d x} [x^{2}] + \frac{d}{d x} [0 x^{3}]$

Step 3.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$0 + 12 - 0.1 (2 x) + \frac{d}{d x} [0 x^{3}]$

Step 3.3

Multiply $2$ by $- 0.1$ .

$0 + 12 - 0.2 x + \frac{d}{d x} [0 x^{3}]$

Step 4

Evaluate $\frac{d}{d x} [0 x^{3}]$ .

Tap for more steps...

Step 4.1

Multiply $0$ by $x^{3}$ .

$0 + 12 - 0.2 x + \frac{d}{d x} [0]$

Step 4.2

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

$0 + 12 - 0.2 x + 0$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Combine terms.

Tap for more steps...

Step 5.1.1

Add $0$ and $12$ .

$12 - 0.2 x + 0$

Step 5.1.2

Add $12 - 0.2 x$ and $0$ .

$12 - 0.2 x$

Step 5.2

Reorder terms.

$- 0.2 x + 12$