Solve x-0frac{sqrt{sinx+1}-1}{x}(1quad)

$$x - 0 \frac { \sqrt { \sin x + 1 } - 1 } { x } ( 1 \quad )$$

Evaluate

$$x$$

Short Solution Steps

Multiply 0 and 1 to get 0.

$$x-0\times \frac{\sqrt{\sin(x)+1}-1}{x}$$

Express 0\times \frac{\sqrt{\sin(x)+1}-1}{x} as a single fraction.

$$x-\frac{0\left(\sqrt{\sin(x)+1}-1\right)}{x}$$

Use the distributive property to multiply 0 by \sqrt{\sin(x)+1}-1.

$$x-\frac{0\sqrt{\sin(x)+1}}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{xx}{x}-\frac{0\sqrt{\sin(x)+1}}{x}$$

Since \frac{xx}{x} and \frac{0\sqrt{\sin(x)+1}}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-0\sqrt{\sin(x)+1}}{x}$$

Do the multiplications in xx-0\sqrt{\sin(x)+1}.

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

Cancel out x in both numerator and denominator.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Multiply 0 and 1 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-0\times \frac{\sqrt{\sin(x)+1}-1}{x})$$

Express 0\times \frac{\sqrt{\sin(x)+1}-1}{x} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-\frac{0\left(\sqrt{\sin(x)+1}-1\right)}{x})$$

Use the distributive property to multiply 0 by \sqrt{\sin(x)+1}-1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-\frac{0\sqrt{\sin(x)+1}}{x})$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xx}{x}-\frac{0\sqrt{\sin(x)+1}}{x})$$

Since \frac{xx}{x} and \frac{0\sqrt{\sin(x)+1}}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xx-0\sqrt{\sin(x)+1}}{x})$$

Do the multiplications in xx-0\sqrt{\sin(x)+1}.

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

Cancel out x in both numerator and denominator.

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$