Solve 24a^2bdiv(-9ab)*(-6a)

$$24 a ^ { 2 } b \div ( - 9 a b ) \times ( - 6 a )$$

Evaluate

$$16a^{2}$$

Solution Steps

Cancel out 3ab in both numerator and denominator.

$$\frac{8a}{-3}\left(-6\right)a$$

Cancel out -3, the greatest common factor in 6 and -3.

$$-2\times 8aa$$

Multiply -2 and 8 to get -16.

$$-16aa$$

Multiply a and a to get a^{2}.

$$-16a^{2}$$

Differentiate w.r.t. a

$$32a$$

Steps Using Definition of a Derivative

Cancel out 3ab in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8a}{-3}\left(-6\right)a)$$

Cancel out -3, the greatest common factor in 6 and -3.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-2\times 8aa)$$

Multiply a and a to get a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-2\times 8a^{2})$$

Multiply -2 and 8 to get -16.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-16a^{2})$$

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

$$2\left(-16\right)a^{2-1}$$

Multiply 2 times -16.

$$-32a^{2-1}$$

Subtract 1 from 2.

$$-32a^{1}$$

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

$$-32a$$