Calculus Examples

$f (x) = 2 x + \frac{3}{- 4}$

Step 1

Differentiate using the Sum Rule.

Tap for more steps...

Step 1.1

Move the negative in front of the fraction.

$\frac{d}{d x} [2 x - \frac{3}{4}]$

Step 1.2

By the Sum Rule, the derivative of $2 x - \frac{3}{4}$ with respect to $x$ is $\frac{d}{d x} [2 x] + \frac{d}{d x} [- \frac{3}{4}]$ .

$\frac{d}{d x} [2 x] + \frac{d}{d x} [- \frac{3}{4}]$

Step 2

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

Tap for more steps...

Step 2.1

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

$2 \frac{d}{d x} [x] + \frac{d}{d x} [- \frac{3}{4}]$

Step 2.2

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

$2 \cdot 1 + \frac{d}{d x} [- \frac{3}{4}]$

Step 2.3

Multiply $2$ by $1$ .

$2 + \frac{d}{d x} [- \frac{3}{4}]$

Step 3

Differentiate using the Constant Rule.

Tap for more steps...

Step 3.1

Since $- \frac{3}{4}$ is constant with respect to $x$ , the derivative of $- \frac{3}{4}$ with respect to $x$ is $0$ .

$2 + 0$

Step 3.2

Add $2$ and $0$ .

$2$