Solve (-sqrt{2x})(sqrt{2x})

$$( - \sqrt { 2 x } ) ( \sqrt { 2 x } )$$

Evaluate

$$-2x$$

Solution Steps

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

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

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

$$-2x$$

Differentiate w.r.t. x

$$-2$$

Steps Using Definition of a Derivative

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x)$$

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

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

Subtract 1 from 1.

$$-2x^{0}$$

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

$$-2$$