Solve 2pir/pir^2

$$\frac { 2 \pi r } { \pi r ^ { 2 } }$$

Differentiate w.r.t. r

$$-\frac{2}{r^{2}}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}r}(2\times \frac{1}{r})$$

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}.

$$-2r^{-1-1}$$

Do the arithmetic.

$$-2r^{-2}$$

Evaluate

$$\frac{2}{r}$$

Solution Steps

Cancel out \pi r in both numerator and denominator.

$$\frac{2}{r}$$