Solve 2sqrt{x}*2sqrt{x}

$$2 \sqrt{ x } \times 2 \sqrt{ x }$$

Evaluate

$$4x$$

Solution Steps

Multiply \sqrt{x} and \sqrt{x} to get \left(\sqrt{x}\right)^{2}.

$$2\times 2\left(\sqrt{x}\right)^{2}$$

Multiply 2 and 2 to get 4.

$$4\left(\sqrt{x}\right)^{2}$$

Calculate \sqrt{x} to the power of 2 and get x.

$$4x$$

Differentiate w.r.t. x

$$4$$

Steps Using Definition of a Derivative

Multiply \sqrt{x} and \sqrt{x} to get \left(\sqrt{x}\right)^{2}.

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

Multiply 2 and 2 to get 4.

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

Calculate \sqrt{x} to the power of 2 and get x.

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

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.

$$4$$