Solve frac{6sqrt{2}}{2}xfrac{-sqrt{2}}{2}

$$\frac { 6 \sqrt { 2 } } { 2 } x \frac { - \sqrt { 2 } } { 2 }$$

Evaluate

$$-3x$$

Solution Steps

Divide 6\sqrt{2} by 2 to get 3\sqrt{2}.

$$3\sqrt{2}x\times \frac{-\sqrt{2}}{2}$$

Express 3\times \frac{-\sqrt{2}}{2} as a single fraction.

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

Express \frac{3\left(-\sqrt{2}\right)}{2}\sqrt{2} as a single fraction.

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

Express \frac{3\left(-\sqrt{2}\right)\sqrt{2}}{2}x as a single fraction.

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

Differentiate w.r.t. x

$$-3$$

Steps Using Definition of a Derivative

Divide 6\sqrt{2} by 2 to get 3\sqrt{2}.

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

Express 3\times \frac{-\sqrt{2}}{2} as a single fraction.

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

Express \frac{3\left(-\sqrt{2}\right)}{2}\sqrt{2} as a single fraction.

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

Express \frac{3\left(-\sqrt{2}\right)\sqrt{2}}{2}x as a single fraction.

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

Multiply 3 and -1 to get -3.

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

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

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

Multiply -3 and 2 to get -6.

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

Divide -6x by 2 to get -3x.

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

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

$$-3x^{1-1}$$

Subtract 1 from 1.

$$-3x^{0}$$

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

$$-3$$