Solve 0-4*-1/8*x

$$0-4 \times - \frac{ 1 }{ 8 } \times x$$

Evaluate

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

Solution Steps

Express 4\left(-\frac{1}{8}\right) as a single fraction.

$$0-\frac{4\left(-1\right)}{8}x$$

Multiply 4 and -1 to get -4.

$$0-\frac{-4}{8}x$$

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

$$0-\left(-\frac{1}{2}x\right)$$

The opposite of -\frac{1}{2}x is \frac{1}{2}x.

$$0+\frac{1}{2}x$$

Anything plus zero gives itself.

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

Differentiate w.r.t. x

$$\frac{1}{2} = 0.5$$

Steps Using Definition of a Derivative

Express 4\left(-\frac{1}{8}\right) as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0-\frac{4\left(-1\right)}{8}x)$$

Multiply 4 and -1 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0-\frac{-4}{8}x)$$

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0-\left(-\frac{1}{2}x\right))$$

The opposite of -\frac{1}{2}x is \frac{1}{2}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0+\frac{1}{2}x)$$

Anything plus zero gives itself.

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

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

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

Subtract 1 from 1.

$$\frac{1}{2}x^{0}$$

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

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

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

$$\frac{1}{2}$$