Solve (a*2/3)*(2a*1/3)

$$( a \cdot \frac { 2 } { 3 } ) \cdot ( 2 a \cdot \frac { 1 } { 3 } )$$

Evaluate

$$\frac{4a^{2}}{9}$$

Solution Steps

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

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

Express \frac{2}{3}\times 2 as a single fraction.

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

Multiply 2 and 2 to get 4.

$$a^{2}\times \frac{4}{3}\times \frac{1}{3}$$

Multiply \frac{4}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$a^{2}\times \frac{4\times 1}{3\times 3}$$

Do the multiplications in the fraction \frac{4\times 1}{3\times 3}.

$$a^{2}\times \frac{4}{9}$$

Differentiate w.r.t. a

$$\frac{8a}{9}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{2}\times \frac{2}{3}\times 2\times \frac{1}{3})$$

Express \frac{2}{3}\times 2 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{2}\times \frac{2\times 2}{3}\times \frac{1}{3})$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{2}\times \frac{4}{3}\times \frac{1}{3})$$

Multiply \frac{4}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{2}\times \frac{4\times 1}{3\times 3})$$

Do the multiplications in the fraction \frac{4\times 1}{3\times 3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{2}\times \frac{4}{9})$$

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

$$2\times \frac{4}{9}a^{2-1}$$

Multiply 2 times \frac{4}{9}.

$$\frac{8}{9}a^{2-1}$$

Subtract 1 from 2.

$$\frac{8}{9}a^{1}$$

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

$$\frac{8}{9}a$$