Calculus Examples

$y = 11 (1) - 3 {(1)}^{4}$

Step 1

Find the first derivative.

Tap for more steps...

Step 1.1

Differentiate using the Sum Rule.

Tap for more steps...

Step 1.1.1

One to any power is one.

$\frac{d}{d x} [11 (1) - 3 \cdot 1]$

Step 1.1.2

By the Sum Rule, the derivative of $11 (1) - 3 \cdot 1$ with respect to $x$ is $\frac{d}{d x} [11 (1)] + \frac{d}{d x} [- 3 \cdot 1]$ .

$\frac{d}{d x} [11 (1)] + \frac{d}{d x} [- 3 \cdot 1]$

Step 1.2

Evaluate $\frac{d}{d x} [11 (1)]$ .

Tap for more steps...

Step 1.2.1

Multiply $11$ by $1$ .

$\frac{d}{d x} [11] + \frac{d}{d x} [- 3 \cdot 1]$

Step 1.2.2

Since $11$ is constant with respect to $x$ , the derivative of $11$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [- 3 \cdot 1]$

Step 1.3

Evaluate $\frac{d}{d x} [- 3 \cdot 1]$ .

Tap for more steps...

Step 1.3.1

Multiply $- 3$ by $1$ .

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

Step 1.3.2

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

$0 + 0$

Step 1.4

Add $0$ and $0$ .

$f' (x) = 0$

Step 2

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

$f'' (x) = 0$

Step 3

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

$f''' (x) = 0$

Step 4

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

$f^{4} (x) = 0$