Solve 2m/5ndiv4m^2/10n

$$\frac { 2 m } { 5 n } \div \frac { 4 m ^ { 2 } } { 10 n }$$

Evaluate

$$\frac{1}{m}$$

Solution Steps

Divide \frac{2m}{5n} by \frac{4m^{2}}{10n} by multiplying \frac{2m}{5n} by the reciprocal of \frac{4m^{2}}{10n}.

$$\frac{2m\times 10n}{5n\times 4m^{2}}$$

Cancel out 2\times 2\times 5mn in both numerator and denominator.

$$\frac{1}{m}$$

Differentiate w.r.t. m

$$-\frac{1}{m^{2}}$$

Steps Using Definition of a Derivative

Divide \frac{2m}{5n} by \frac{4m^{2}}{10n} by multiplying \frac{2m}{5n} by the reciprocal of \frac{4m^{2}}{10n}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{2m\times 10n}{5n\times 4m^{2}})$$

Cancel out 2\times 2\times 5mn in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1}{m})$$

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

$$-m^{-1-1}$$

Subtract 1 from -1.

$$-m^{-2}$$