Find the Derivative - d/dx x^(10/11)

$x^{\frac{10}{11}}$

Step 1

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = \frac{10}{11}$ .

$\frac{10}{11} x^{\frac{10}{11} - 1}$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{10}{11} x^{\frac{10}{11} - 1 \cdot \frac{11}{11}}$

Step 3

Combine $- 1$ and $\frac{11}{11}$ .

$\frac{10}{11} x^{\frac{10}{11} + \frac{- 1 \cdot 11}{11}}$

Step 4

Combine the numerators over the common denominator.

$\frac{10}{11} x^{\frac{10 - 1 \cdot 11}{11}}$

Step 5

Simplify the numerator.

Multiply $- 1$ by $11$ .

$\frac{10}{11} x^{\frac{10 - 11}{11}}$

Subtract $11$ from $10$ .

$\frac{10}{11} x^{\frac{- 1}{11}}$

Step 6

Move the negative in front of the fraction.

$\frac{10}{11} x^{- \frac{1}{11}}$

Step 7

Simplify.

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{10}{11} \cdot \frac{1}{x^{\frac{1}{11}}}$

Multiply $\frac{10}{11}$ by $\frac{1}{x^{\frac{1}{11}}}$ .

$\frac{10}{11 x^{\frac{1}{11}}}$