Solve 4/5x|1/6=

$$4 / 5 x | 1 / 6 =$$

Evaluate

$$\frac{2x}{15}$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{1}{6} is \frac{1}{6}.

$$\frac{4}{5}x\times \frac{1}{6}$$

Multiply \frac{4}{5} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 1}{5\times 6}x$$

Do the multiplications in the fraction \frac{4\times 1}{5\times 6}.

$$\frac{4}{30}x$$

Reduce the fraction \frac{4}{30} to lowest terms by extracting and canceling out 2.

$$\frac{2}{15}x$$

Differentiate w.r.t. x

$$\frac{2}{15} = 0.13333333333333333$$

Steps Using Definition of a Derivative

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{1}{6} is \frac{1}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{5}x\times \frac{1}{6})$$

Multiply \frac{4}{5} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 1}{5\times 6}x)$$

Do the multiplications in the fraction \frac{4\times 1}{5\times 6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{30}x)$$

Reduce the fraction \frac{4}{30} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{15}x)$$

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

$$\frac{2}{15}x^{1-1}$$

Subtract 1 from 1.

$$\frac{2}{15}x^{0}$$

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

$$\frac{2}{15}\times 1$$

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

$$\frac{2}{15}$$