Solve 2pi100/xdivpi

$$2 \pi \frac{ 100 }{ x } \div \pi$$

Evaluate

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

Solution Steps

Cancel out \pi and \pi .

$$2\times \frac{100}{x}$$

Express 2\times \frac{100}{x} as a single fraction.

$$\frac{2\times 100}{x}$$

Multiply 2 and 100 to get 200.

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

Differentiate w.r.t. x

$$-\frac{200}{x^{2}}$$

Steps Using Definition of a Derivative

Cancel out \pi and \pi .

$$\frac{\mathrm{d}}{\mathrm{d}x}(2\times \frac{100}{x})$$

Express 2\times \frac{100}{x} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\times 100}{x})$$

Multiply 2 and 100 to get 200.

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

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

$$-200x^{-1-1}$$

Subtract 1 from -1.

$$-200x^{-2}$$