Solve 12a^2/3bdiv4ab

$$\frac { 12 a ^ { 2 } } { 3 b } \div 4 a b$$

Evaluate

$$a^{3}$$

Solution Steps

Express \frac{\frac{12a^{2}}{3b}}{4} as a single fraction.

$$\frac{12a^{2}}{3b\times 4}ab$$

Cancel out 3\times 4 in both numerator and denominator.

$$\frac{a^{2}}{b}ab$$

Express \frac{a^{2}}{b}a as a single fraction.

$$\frac{a^{2}a}{b}b$$

Cancel out b and b.

$$a^{2}a$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$a^{3}$$

Differentiate w.r.t. a

$$3a^{2}$$

Steps Using Definition of a Derivative

Express \frac{\frac{12a^{2}}{3b}}{4} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{12a^{2}}{3b\times 4}ab)$$

Cancel out 3\times 4 in both numerator and denominator.

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

Express \frac{a^{2}}{b}a as a single fraction.

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

Cancel out b and b.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

$$3a^{3-1}$$

Subtract 1 from 3.

$$3a^{2}$$