Solve sqrt{x}*-2xsqrt{x}

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

Evaluate

$$-2x^{2}$$

Solution Steps

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

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

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

$$x\left(-2\right)x$$

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

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

Differentiate w.r.t. x

$$-4x$$

Steps Using Definition of a Derivative

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

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

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

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

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

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

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

$$2\left(-2\right)x^{2-1}$$

Multiply 2 times -2.

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

Subtract 1 from 2.

$$-4x^{1}$$

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

$$-4x$$