Calculus Examples

$x^{n + 1}$

Step 1

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

$(n + 1) x^{n + 1 - 1}$

Step 2

Simplify by subtracting numbers.

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Step 2.1

Subtract $1$ from $1$ .

$(n + 1) x^{n + 0}$

Step 2.2

Add $n$ and $0$ .

$(n + 1) x^{n}$

Step 3

Simplify.

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Step 3.1

Apply the distributive property.

$n x^{n} + 1 x^{n}$

Step 3.2

Multiply $x^{n}$ by $1$ .

$n x^{n} + x^{n}$

Step 3.3

Reorder terms.

$x^{n} n + x^{n}$

Step 3.4

Reorder factors in $x^{n} n + x^{n}$ .

$n x^{n} + x^{n}$