Solve (-25/9ab^4c^3):(-10/21ab^2c^3)

$$( - \frac { 25 } { 9 } a b ^ { 4 } c ^ { 3 } ) : ( - \frac { 10 } { 21 } a b ^ { 2 } c ^ { 3 } )$$

Evaluate

$$\frac{35b^{2}}{6}$$

Solution Steps

Cancel out ab^{2}c^{3} in both numerator and denominator.

$$\frac{-\frac{25}{9}b^{2}}{-\frac{10}{21}}$$

Divide -\frac{25}{9}b^{2} by -\frac{10}{21} by multiplying -\frac{25}{9}b^{2} by the reciprocal of -\frac{10}{21}.

$$\frac{-\frac{25}{9}b^{2}\times 21}{-10}$$

Multiply -\frac{25}{9} and 21 to get -\frac{175}{3}.

$$\frac{-\frac{175}{3}b^{2}}{-10}$$

Divide -\frac{175}{3}b^{2} by -10 to get \frac{35}{6}b^{2}.

$$\frac{35}{6}b^{2}$$

Differentiate w.r.t. b

$$\frac{35b}{3}$$

Steps Using Definition of a Derivative

Cancel out ab^{2}c^{3} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{-\frac{25}{9}b^{2}}{-\frac{10}{21}})$$

Divide -\frac{25}{9}b^{2} by -\frac{10}{21} by multiplying -\frac{25}{9}b^{2} by the reciprocal of -\frac{10}{21}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{-\frac{25}{9}b^{2}\times 21}{-10})$$

Multiply -\frac{25}{9} and 21 to get -\frac{175}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{-\frac{175}{3}b^{2}}{-10})$$

Divide -\frac{175}{3}b^{2} by -10 to get \frac{35}{6}b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{35}{6}b^{2})$$

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

$$2\times \frac{35}{6}b^{2-1}$$

Multiply 2 times \frac{35}{6}.

$$\frac{35}{3}b^{2-1}$$

Subtract 1 from 2.

$$\frac{35}{3}b^{1}$$

For any term t, t^{1}=t.

$$\frac{35}{3}b$$