Solve 1/3x(-2x)

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

Evaluate

$$-\frac{2x^{2}}{3}$$

Solution Steps

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

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

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

$$\frac{-2}{3}x^{2}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$-\frac{2}{3}x^{2}$$

Differentiate w.r.t. x

$$-\frac{4x}{3}$$

Steps Using Definition of a Derivative

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

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

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

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

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

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

Multiply 2 times -\frac{2}{3}.

$$-\frac{4}{3}x^{2-1}$$

Subtract 1 from 2.

$$-\frac{4}{3}x^{1}$$

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

$$-\frac{4}{3}x$$