Solve d/x1/8x

$$\frac { d } { x } \frac { 1 } { 8 } x$$

Evaluate

$$\frac{d}{8}$$

Solution Steps

Multiply \frac{d}{x} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{d}{x\times 8}x$$

Express \frac{d}{x\times 8}x as a single fraction.

$$\frac{dx}{x\times 8}$$

Cancel out x in both numerator and denominator.

$$\frac{d}{8}$$

Differentiate w.r.t. d

$$\frac{1}{8} = 0.125$$

Steps Using Definition of a Derivative

Multiply \frac{d}{x} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

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

Express \frac{d}{x\times 8}x as a single fraction.

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

Cancel out x in both numerator and denominator.

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

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

$$\frac{1}{8}d^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{8}d^{0}$$

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

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

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

$$\frac{1}{8}$$