Solve 2x^frac{2-4{9}}=

$$2 x ^ { \frac { 2 - 4 } { 9 } } =$$

Evaluate

$$\frac{2}{x^{\frac{2}{9}}}$$

Solution Steps

Subtract 4 from 2 to get -2.

$$2x^{\frac{-2}{9}}$$

Fraction \frac{-2}{9} can be rewritten as -\frac{2}{9} by extracting the negative sign.

$$2x^{-\frac{2}{9}}$$

Differentiate w.r.t. x

$$-\frac{4}{9x^{\frac{11}{9}}}$$

Steps Using Definition of a Derivative

Subtract 4 from 2 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{\frac{-2}{9}})$$

Fraction \frac{-2}{9} can be rewritten as -\frac{2}{9} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{-\frac{2}{9}})$$

The derivative of ax^{n} is nax^{n-1}.

$$-\frac{2}{9}\times 2x^{-\frac{2}{9}-1}$$

Multiply -\frac{2}{9} times 2.

$$-\frac{4}{9}x^{-\frac{2}{9}-1}$$

Subtract 1 from -\frac{2}{9}.

$$-\frac{4}{9}x^{-\frac{11}{9}}$$