Solve (x*2)*(x*2)

$$(x \times 2) \times (x \times 2)$$

Evaluate

$$4x^{2}$$

Solution Steps

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

$$x^{2}\times 2\times 2$$

Multiply 2 and 2 to get 4.

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

Differentiate w.r.t. x

$$8x$$

Steps Using Definition of a Derivative

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

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

Multiply 2 and 2 to get 4.

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

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.

$$8x$$