Calculus Examples

$y = x^{\frac{9}{5}}$

Step 1

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = \frac{9}{5}$ .

$\frac{9}{5} x^{\frac{9}{5} - 1}$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9}{5} x^{\frac{9}{5} - 1 \cdot \frac{5}{5}}$

Step 3

Combine $- 1$ and $\frac{5}{5}$ .

$\frac{9}{5} x^{\frac{9}{5} + \frac{- 1 \cdot 5}{5}}$

Step 4

Combine the numerators over the common denominator.

$\frac{9}{5} x^{\frac{9 - 1 \cdot 5}{5}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 1$ by $5$ .

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

Step 5.2

Subtract $5$ from $9$ .

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

Step 6

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

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