Solve 2pi(100/xpi)

$$2 \pi ( \frac{ 100 }{ x \pi } )$$

Evaluate

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

Solution Steps

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

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

Multiply 2 and 100 to get 200.

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

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

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

Cancel out \pi in both numerator and denominator.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

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

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

Multiply 2 and 100 to get 200.

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

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

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

Cancel out \pi in both numerator and denominator.

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

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

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

Subtract 1 from -1.

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