Calculus Examples

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

Step 1

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

$\frac{1}{n + 1} \frac{d}{d x} [x^{n + 1}]$

Step 2

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

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

Step 3

Combine fractions.

Tap for more steps...

Step 3.1

Subtract $1$ from $1$ .

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

Step 3.2

Add $n$ and $0$ .

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

Step 3.3

Combine $x^{n}$ and $\frac{1}{n + 1}$ .

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

Reorder the factors of $\frac{x^{n}}{n + 1} (n + 1)$ .

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

Step 4.2

Cancel the common factor of $n + 1$ .

Tap for more steps...

Step 4.2.1

Cancel the common factor.

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

Step 4.2.2

Rewrite the expression.

$x^{n}$