Solve x/2(-1/4)

$$\frac { x } { 2 ( - 1 / 4 ) }$$

Evaluate

$$-2x$$

Solution Steps

Express 2\left(-\frac{1}{4}\right) as a single fraction.

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

Multiply 2 and -1 to get -2.

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

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

$$\frac{x}{-\frac{1}{2}}$$

Divide x by -\frac{1}{2} by multiplying x by the reciprocal of -\frac{1}{2}.

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

Anything divided by -1 gives its opposite.

$$-x\times 2$$

Multiply -1 and 2 to get -2.

$$-2x$$

Differentiate w.r.t. x

$$-2$$

Steps Using Definition of a Derivative

Express 2\left(-\frac{1}{4}\right) as a single fraction.

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

Multiply 2 and -1 to get -2.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{-\frac{1}{2}})$$

Divide x by -\frac{1}{2} by multiplying x by the reciprocal of -\frac{1}{2}.

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

Anything divided by -1 gives its opposite.

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

Multiply -1 and 2 to get -2.

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

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

$$-2x^{1-1}$$

Subtract 1 from 1.

$$-2x^{0}$$

For any term t except 0, t^{0}=1.

$$-2$$