Solve 3/xquad(3)sqrt{2^2}

$$\frac { 3 } { x } \quad ( 3 ) \sqrt { 2 ^ { 2 } }$$

Evaluate

$$\frac{18}{x}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{3}{x}\times 3\sqrt{4}$$

Calculate the square root of 4 and get 2.

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

Multiply 3 and 2 to get 6.

$$\frac{3}{x}\times 6$$

Express \frac{3}{x}\times 6 as a single fraction.

$$\frac{3\times 6}{x}$$

Multiply 3 and 6 to get 18.

$$\frac{18}{x}$$

Differentiate w.r.t. x

$$-\frac{18}{x^{2}}$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 2 and get 4.

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

Calculate the square root of 4 and get 2.

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

Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{x}\times 6)$$

Express \frac{3}{x}\times 6 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\times 6}{x})$$

Multiply 3 and 6 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18}{x})$$

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

$$-18x^{-1-1}$$

Subtract 1 from -1.

$$-18x^{-2}$$