Solve (sqrt{3}*sqrt{2}x)(-sqrt{2}*sqrt{3}x)

$$( \sqrt{ 3 } \times \sqrt{ 2 } x)(- \sqrt{ 2 } \times \sqrt{ 3 } x)$$

Evaluate

$$-6x^{2}$$

Solution Steps

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\sqrt{2}x\left(-\sqrt{2}\right)x$$

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

$$3\sqrt{2}x^{2}\left(-\sqrt{2}\right)$$

Differentiate w.r.t. x

$$-12x$$

Steps Using Definition of a Derivative

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3\sqrt{2}x\left(-\sqrt{2}\right)x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(3\sqrt{2}x^{2}\left(-\sqrt{2}\right))$$

Multiply 3 and -1 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3\sqrt{2}x^{2}\sqrt{2})$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply -3 and 2 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{2})$$

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

$$2\left(-6\right)x^{2-1}$$

Multiply 2 times -6.

$$-12x^{2-1}$$

Subtract 1 from 2.

$$-12x^{1}$$

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

$$-12x$$