Solve x/8*3/9

$$\frac { x } { 8 } \times \frac { 3 } { 9 }$$

Evaluate

$$\frac{x}{24}$$

Solution Steps

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{x}{8}\times \frac{1}{3}$$

Multiply \frac{x}{8} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{8\times 3}$$

Multiply 8 and 3 to get 24.

$$\frac{x}{24}$$

Differentiate w.r.t. x

$$\frac{1}{24} = 0.041666666666666664$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{8}\times \frac{1}{3})$$

Multiply \frac{x}{8} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{8\times 3})$$

Multiply 8 and 3 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{24})$$

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

$$\frac{1}{24}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{24}x^{0}$$

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

$$\frac{1}{24}\times 1$$

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

$$\frac{1}{24}$$