Solve 8pix/x^2

$$\frac { 8 \pi x } { x ^ { 2 } }$$

Differentiate w.r.t. x

$$-\frac{8\pi }{x^{2}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8\pi }{1}x^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8\pi \times \frac{1}{x})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-8\pi x^{-1-1}$$

Do the arithmetic.

$$\left(-8\pi \right)x^{-2}$$

Evaluate

$$\frac{8\pi }{x}$$

Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{8\pi }{x}$$