Solve x%22/5588

$$\frac{ x \% 22 }{ 5588 }$$

Evaluate

$$\frac{x}{25400}$$

Solution Steps

Express \frac{x}{100}\times 22 as a single fraction.

$$\frac{\frac{x\times 22}{100}}{5588}$$

Express \frac{\frac{x\times 22}{100}}{5588} as a single fraction.

$$\frac{x\times 22}{100\times 5588}$$

Cancel out 2\times 11 in both numerator and denominator.

$$\frac{x}{50\times 508}$$

Multiply 50 and 508 to get 25400.

$$\frac{x}{25400}$$

Differentiate w.r.t. x

$$\frac{1}{25400} = 3.9370078740157477 \times 10^{-5}$$

Steps Using Definition of a Derivative

Express \frac{x}{100}\times 22 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x\times 22}{100}}{5588})$$

Express \frac{\frac{x\times 22}{100}}{5588} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\times 22}{100\times 5588})$$

Cancel out 2\times 11 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{50\times 508})$$

Multiply 50 and 508 to get 25400.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{25400})$$

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

$$\frac{1}{25400}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{25400}x^{0}$$

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

$$\frac{1}{25400}\times 1$$

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

$$\frac{1}{25400}$$