Solve 3(2)(2/3x)

$$3 ( 2 ) ( \frac { 2 } { 3 } x )$$

Evaluate

$$4x$$

Solution Steps

Multiply 3 and 2 to get 6.

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

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

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

Multiply 6 and 2 to get 12.

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

Divide 12 by 3 to get 4.

$$4x$$

Differentiate w.r.t. x

$$4$$

Steps Using Definition of a Derivative

Multiply 3 and 2 to get 6.

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

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

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

Multiply 6 and 2 to get 12.

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

Divide 12 by 3 to get 4.

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

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

$$4x^{1-1}$$

Subtract 1 from 1.

$$4x^{0}$$

For any term t except 0, t^{0}=1.

$$4\times 1$$

For any term t, t\times 1=t and 1t=t.

$$4$$