Solve -4/3sqrt{18}div2sqrt{8}x

$$- \frac { 4 } { 3 } \sqrt { 18 } \div 2 \sqrt { 8 } x$$

Evaluate

$$-8x$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{-\frac{4}{3}\times 3\sqrt{2}}{2}\sqrt{8}x$$

Cancel out 3 and 3.

$$\frac{-4\sqrt{2}}{2}\sqrt{8}x$$

Divide -4\sqrt{2} by 2 to get -2\sqrt{2}.

$$-2\sqrt{2}\sqrt{8}x$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Multiply -2 and 2 to get -4.

$$-4\sqrt{2}\sqrt{2}x$$

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

$$-4\times 2x$$

Multiply -4 and 2 to get -8.

$$-8x$$

Differentiate w.r.t. x

$$-8$$

Steps Using Definition of a Derivative

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{4}{3}\times 3\sqrt{2}}{2}\sqrt{8}x)$$

Cancel out 3 and 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-4\sqrt{2}}{2}\sqrt{8}x)$$

Divide -4\sqrt{2} by 2 to get -2\sqrt{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2\sqrt{2}\sqrt{8}x)$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Multiply -2 and 2 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4\sqrt{2}\sqrt{2}x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4\times 2x)$$

Multiply -4 and 2 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8x)$$

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

$$-8x^{1-1}$$

Subtract 1 from 1.

$$-8x^{0}$$

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

$$-8$$