Solve 2/4x2/6

$$\frac { 2 } { 4 } x \frac { 2 } { 6 }$$

Evaluate

$$\frac{x}{6}$$

Solution Steps

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

$$\frac{1}{2}x\times \frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}x\times \frac{1}{3}$$

Multiply \frac{1}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{2\times 3}x$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 3}.

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

Differentiate w.r.t. x

$$\frac{1}{6} = 0.16666666666666666$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x\times \frac{2}{6})$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x\times \frac{1}{3})$$

Multiply \frac{1}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1\times 1}{2\times 3}x)$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 3}.

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

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

$$\frac{1}{6}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{6}x^{0}$$

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

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

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

$$\frac{1}{6}$$