Solve (7/426/7)x]

$$( 7 / 42 \frac { 6 } { 7 } ) x ]$$

Evaluate

$$\frac{x}{7}$$

Solution Steps

Reduce the fraction \frac{7}{42} to lowest terms by extracting and canceling out 7.

$$\frac{1}{6}\times \frac{6}{7}x$$

Multiply \frac{1}{6} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 6}{6\times 7}x$$

Cancel out 6 in both numerator and denominator.

$$\frac{1}{7}x$$

Differentiate w.r.t. x

$$\frac{1}{7} = 0.14285714285714285$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{7}{42} to lowest terms by extracting and canceling out 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{6}\times \frac{6}{7}x)$$

Multiply \frac{1}{6} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1\times 6}{6\times 7}x)$$

Cancel out 6 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{7}x)$$

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

$$\frac{1}{7}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{7}x^{0}$$

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

$$\frac{1}{7}\times 1$$

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

$$\frac{1}{7}$$