Solve 2a^2/3bdiv4ab

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

Evaluate

$$\frac{a^{3}}{6}$$

Solution Steps

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

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

Cancel out 2 in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

$$\frac{a^{2}}{6b}ab$$

Express \frac{a^{2}}{6b}a as a single fraction.

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

Express \frac{a^{2}a}{6b}b as a single fraction.

$$\frac{a^{2}ab}{6b}$$

Cancel out b in both numerator and denominator.

$$\frac{aa^{2}}{6}$$

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

$$\frac{a^{3}}{6}$$

Differentiate w.r.t. a

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

Steps Using Definition of a Derivative

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

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

Cancel out 2 in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

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

Express \frac{a^{2}}{6b}a as a single fraction.

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

Express \frac{a^{2}a}{6b}b as a single fraction.

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

Cancel out b in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{aa^{2}}{6})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{3}}{6})$$

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

$$3\times \frac{1}{6}a^{3-1}$$

Multiply 3 times \frac{1}{6}.

$$\frac{1}{2}a^{3-1}$$

Subtract 1 from 3.

$$\frac{1}{2}a^{2}$$