Solve (-1/3)^3x(2/3x)

$$( \frac { - 1 } { 3 } ) ^ { 3 } x ( \frac { 2 } { 3 } x )$$

Evaluate

$$-\frac{2x^{2}}{81}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\left(\frac{-1}{3}\right)^{3}x^{2}\times \frac{2}{3}$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$\left(-\frac{1}{3}\right)^{3}x^{2}\times \frac{2}{3}$$

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$-\frac{1}{27}x^{2}\times \frac{2}{3}$$

Multiply -\frac{1}{27} and \frac{2}{3} to get -\frac{2}{81}.

$$-\frac{2}{81}x^{2}$$

Differentiate w.r.t. x

$$-\frac{4x}{81}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(\frac{-1}{3}\right)^{3}x^{2}\times \frac{2}{3})$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{1}{3}\right)^{3}x^{2}\times \frac{2}{3})$$

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{27}x^{2}\times \frac{2}{3})$$

Multiply -\frac{1}{27} and \frac{2}{3} to get -\frac{2}{81}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{2}{81}x^{2})$$

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

$$2\left(-\frac{2}{81}\right)x^{2-1}$$

Multiply 2 times -\frac{2}{81}.

$$-\frac{4}{81}x^{2-1}$$

Subtract 1 from 2.

$$-\frac{4}{81}x^{1}$$

For any term t, t^{1}=t.

$$-\frac{4}{81}x$$