Solve frac{frac{frac{frac{frac{frac{frac{frac{frac{frac{frac{frac{x/xx/xx/xx/xx}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x2}{2x}2x}{2x}

$$\frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ x }{ x } x }{ x } x }{ x } x }{ x } x }{ x } x }{ x } x }{ x } x }{ x } x }{ x } x }{ x } x }{ x } x }{ x } x }{ x } x }{ x } x2 }{ 2x } 2x }{ 2x }$$

Evaluate

$$\frac{x_{2}}{2x}$$

Solution Steps

Divide x by x to get 1.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x_{2}}{2x}\times 2x}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x_{2}}{2x}\times 2x}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x_{2}}{2x}\times 2x}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x_{2}}{2x}\times 2x}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x_{2}}{2x}\times 2x}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x_{2}}{2x}\times 2x}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x_{2}}{2x}\times 2x}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x_{2}}{2x}\times 2x}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{1x}{x}x}{x}x}{x}x}{x}x}{x}x_{2}}{2x}\times 2x}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{\frac{\frac{\frac{\frac{1x}{x}x}{x}x}{x}x}{x}x_{2}}{2x}\times 2x}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{\frac{\frac{\frac{1x}{x}x}{x}x}{x}x_{2}}{2x}\times 2x}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{\frac{\frac{1x}{x}x}{x}x_{2}}{2x}\times 2x}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{\frac{1x}{x}x_{2}}{2x}\times 2x}{2x}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{1x_{2}}{2x}\times 2x}{2x}$$

Cancel out 1 in both numerator and denominator.

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

Express \frac{x_{2}}{2x}\times 2 as a single fraction.

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

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{x_{2}}{x}x}{2x}$$

Cancel out x and x.

$$\frac{x_{2}}{2x}$$

Differentiate w.r.t. x

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

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\times \frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x}{x}x_{2}}{2x}}{2}x^{1-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x_{2}}{2x}x^{0})$$

For any number a except 0, a^{0}=1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x_{2}}{2x})$$

The derivative of a constant term is 0.

$$0$$