Calculus Examples

$x^{\frac{9}{4}}$

Step 1

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = \frac{9}{4}$ .

$\frac{9}{4} x^{\frac{9}{4} - 1}$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9}{4} x^{\frac{9}{4} - 1 \cdot \frac{4}{4}}$

Step 3

Combine $- 1$ and $\frac{4}{4}$ .

$\frac{9}{4} x^{\frac{9}{4} + \frac{- 1 \cdot 4}{4}}$

Step 4

Combine the numerators over the common denominator.

$\frac{9}{4} x^{\frac{9 - 1 \cdot 4}{4}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 1$ by $4$ .

$\frac{9}{4} x^{\frac{9 - 4}{4}}$

Step 5.2

Subtract $4$ from $9$ .

$\frac{9}{4} x^{\frac{5}{4}}$

Step 6

Combine $\frac{9}{4}$ and $x^{\frac{5}{4}}$ .

$\frac{9 x^{\frac{5}{4}}}{4}$