Solve 21/n/frac{7{16}}

$$\frac { \frac { 21 } { n } } { \frac { 7 } { 16 } }$$

Evaluate

$$\frac{48}{n}$$

Solution Steps

Divide \frac{21}{n} by \frac{7}{16} by multiplying \frac{21}{n} by the reciprocal of \frac{7}{16}.

$$\frac{21\times 16}{n\times 7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{3\times 16}{n}$$

Multiply 3 and 16 to get 48.

$$\frac{48}{n}$$

Differentiate w.r.t. n

$$-\frac{48}{n^{2}}$$

Steps Using Definition of a Derivative

Divide \frac{21}{n} by \frac{7}{16} by multiplying \frac{21}{n} by the reciprocal of \frac{7}{16}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{21\times 16}{n\times 7})$$

Cancel out 7 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{3\times 16}{n})$$

Multiply 3 and 16 to get 48.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{48}{n})$$

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

$$-48n^{-1-1}$$

Subtract 1 from -1.

$$-48n^{-2}$$