Solve 2/3x*6x

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

Evaluate

$$4x^{2}$$

Solution Steps

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

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

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

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

Multiply 2 and 6 to get 12.

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

Divide 12 by 3 to get 4.

$$4x^{2}$$

Differentiate w.r.t. x

$$8x$$

Steps Using Definition of a Derivative

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

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

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

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

Multiply 2 and 6 to get 12.

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

Divide 12 by 3 to get 4.

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

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

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

Multiply 2 times 4.

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

Subtract 1 from 2.

$$8x^{1}$$

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

$$8x$$