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

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

Evaluate

$$\frac{x}{4}$$

Solution Steps

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{1}{8}x|-2|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

$$\frac{1}{8}x\times 2$$

Multiply \frac{1}{8} and 2 to get \frac{2}{8}.

$$\frac{2}{8}x$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}x$$

Differentiate w.r.t. x

$$\frac{1}{4} = 0.25$$

Steps Using Definition of a Derivative

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{8}x|-2|)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{8}x\times 2)$$

Multiply \frac{1}{8} and 2 to get \frac{2}{8}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{8}x)$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4}x)$$

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

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

Subtract 1 from 1.

$$\frac{1}{4}x^{0}$$

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

$$\frac{1}{4}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{4}$$