Solve x:20:6:8

$$x : 20 : 6 : 8$$

Evaluate

$$\frac{x}{960}$$

Solution Steps

Express \frac{\frac{\frac{x}{20}}{6}}{8} as a single fraction.

$$\frac{\frac{x}{20}}{6\times 8}$$

Multiply 6 and 8 to get 48.

$$\frac{\frac{x}{20}}{48}$$

Express \frac{\frac{x}{20}}{48} as a single fraction.

$$\frac{x}{20\times 48}$$

Multiply 20 and 48 to get 960.

$$\frac{x}{960}$$

Differentiate w.r.t. x

$$\frac{1}{960} = 0.0010416666666666667$$

Steps Using Definition of a Derivative

Express \frac{\frac{\frac{x}{20}}{6}}{8} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{20}}{6\times 8})$$

Multiply 6 and 8 to get 48.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{20}}{48})$$

Express \frac{\frac{x}{20}}{48} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{20\times 48})$$

Multiply 20 and 48 to get 960.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{960})$$

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

$$\frac{1}{960}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{960}x^{0}$$

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

$$\frac{1}{960}\times 1$$

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

$$\frac{1}{960}$$