Solve 14m^4/3mdiv7m^2/18m^5

$$\frac { 14 m ^ { 4 } } { 3 m } \div \frac { 7 m ^ { 2 } } { 18 m ^ { 5 } }$$

Evaluate

$$12m^{6}$$

Solution Steps

Divide \frac{14m^{4}}{3m} by \frac{7m^{2}}{18m^{5}} by multiplying \frac{14m^{4}}{3m} by the reciprocal of \frac{7m^{2}}{18m^{5}}.

$$\frac{14m^{4}\times 18m^{5}}{3m\times 7m^{2}}$$

Cancel out 3\times 7mm^{2} in both numerator and denominator.

$$2\times 6mm^{5}$$

Multiply 2 and 6 to get 12.

$$12mm^{5}$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$12m^{6}$$

Differentiate w.r.t. m

$$72m^{5}$$

Steps Using Definition of a Derivative

Divide \frac{14m^{4}}{3m} by \frac{7m^{2}}{18m^{5}} by multiplying \frac{14m^{4}}{3m} by the reciprocal of \frac{7m^{2}}{18m^{5}}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{14m^{4}\times 18m^{5}}{3m\times 7m^{2}})$$

Cancel out 3\times 7mm^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}m}(2\times 6mm^{5})$$

Multiply 2 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}m}(12mm^{5})$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}m}(12m^{6})$$

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

$$6\times 12m^{6-1}$$

Multiply 6 times 12.

$$72m^{6-1}$$

Subtract 1 from 6.

$$72m^{5}$$