Solve 2/3a*6a

$$\frac { 2 } { 3 } a \times 6 a$$

Evaluate

$$4a^{2}$$

Solution Steps

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

$$\frac{2}{3}a^{2}\times 6$$

Express \frac{2}{3}\times 6 as a single fraction.

$$\frac{2\times 6}{3}a^{2}$$

Multiply 2 and 6 to get 12.

$$\frac{12}{3}a^{2}$$

Divide 12 by 3 to get 4.

$$4a^{2}$$

Differentiate w.r.t. a

$$8a$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2}{3}a^{2}\times 6)$$

Express \frac{2}{3}\times 6 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2\times 6}{3}a^{2})$$

Multiply 2 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{12}{3}a^{2})$$

Divide 12 by 3 to get 4.

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

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

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

Multiply 2 times 4.

$$8a^{2-1}$$

Subtract 1 from 2.

$$8a^{1}$$

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

$$8a$$