Solve x:75:25:15

$$x : 75 : 25 : 15$$

Evaluate

$$\frac{x}{28125}$$

Solution Steps

Express \frac{\frac{\frac{x}{75}}{25}}{15} as a single fraction.

$$\frac{\frac{x}{75}}{25\times 15}$$

Multiply 25 and 15 to get 375.

$$\frac{\frac{x}{75}}{375}$$

Express \frac{\frac{x}{75}}{375} as a single fraction.

$$\frac{x}{75\times 375}$$

Multiply 75 and 375 to get 28125.

$$\frac{x}{28125}$$

Differentiate w.r.t. x

$$\frac{1}{28125} = 3.555555555555555 \times 10^{-5}$$

Steps Using Definition of a Derivative

Express \frac{\frac{\frac{x}{75}}{25}}{15} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{75}}{25\times 15})$$

Multiply 25 and 15 to get 375.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{75}}{375})$$

Express \frac{\frac{x}{75}}{375} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{75\times 375})$$

Multiply 75 and 375 to get 28125.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{28125})$$

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

$$\frac{1}{28125}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{28125}x^{0}$$

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

$$\frac{1}{28125}\times 1$$

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

$$\frac{1}{28125}$$