Solve 1/2x*-4/3x

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

Evaluate

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

Solution Steps

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

$$\frac{1}{2}x^{2}\left(-\frac{4}{3}\right)$$

Multiply \frac{1}{2} times -\frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-4\right)}{2\times 3}x^{2}$$

Do the multiplications in the fraction \frac{1\left(-4\right)}{2\times 3}.

$$\frac{-4}{6}x^{2}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{2}\left(-\frac{4}{3}\right))$$

Multiply \frac{1}{2} times -\frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1\left(-4\right)}{2\times 3}x^{2})$$

Do the multiplications in the fraction \frac{1\left(-4\right)}{2\times 3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-4}{6}x^{2})$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

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

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.

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