Solve -18a^2bdiv(-6ab^2)*3ab

$$- 18 a ^ { 2 } b \div ( - 6 a b ^ { 2 } ) \times 3 a b$$

Evaluate

$$9a^{2}$$

Solution Steps

Cancel out 6ab in both numerator and denominator.

$$\frac{-3a}{-b}\times 3ab$$

Cancel out -1 in both numerator and denominator.

$$\frac{3a}{b}\times 3ab$$

Express \frac{3a}{b}\times 3 as a single fraction.

$$\frac{3a\times 3}{b}ab$$

Express \frac{3a\times 3}{b}a as a single fraction.

$$\frac{3a\times 3a}{b}b$$

Cancel out b and b.

$$3a\times 3a$$

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

$$3a^{2}\times 3$$

Multiply 3 and 3 to get 9.

$$9a^{2}$$

Differentiate w.r.t. a

$$18a$$

Steps Using Definition of a Derivative

Cancel out 6ab in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-3a}{-b}\times 3ab)$$

Cancel out -1 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3a}{b}\times 3ab)$$

Express \frac{3a}{b}\times 3 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3a\times 3}{b}ab)$$

Express \frac{3a\times 3}{b}a as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3a\times 3a}{b}b)$$

Cancel out b and b.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a\times 3a)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{2}\times 3)$$

Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}a}(9a^{2})$$

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

$$2\times 9a^{2-1}$$

Multiply 2 times 9.

$$18a^{2-1}$$

Subtract 1 from 2.

$$18a^{1}$$

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

$$18a$$