Solve x:250:4:50

$$x : 250 : 4 : 50$$

Evaluate

$$\frac{x}{50000}$$

Solution Steps

Express \frac{\frac{\frac{x}{250}}{4}}{50} as a single fraction.

$$\frac{\frac{x}{250}}{4\times 50}$$

Multiply 4 and 50 to get 200.

$$\frac{\frac{x}{250}}{200}$$

Express \frac{\frac{x}{250}}{200} as a single fraction.

$$\frac{x}{250\times 200}$$

Multiply 250 and 200 to get 50000.

$$\frac{x}{50000}$$

Differentiate w.r.t. x

$$\frac{1}{50000} = 2 \times 10^{-5}$$

Steps Using Definition of a Derivative

Express \frac{\frac{\frac{x}{250}}{4}}{50} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{250}}{4\times 50})$$

Multiply 4 and 50 to get 200.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{250}}{200})$$

Express \frac{\frac{x}{250}}{200} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{250\times 200})$$

Multiply 250 and 200 to get 50000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{50000})$$

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

$$\frac{1}{50000}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{50000}x^{0}$$

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

$$\frac{1}{50000}\times 1$$

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

$$\frac{1}{50000}$$