Solve (sqrt{x+1})^2-(1)^2

$$( \sqrt { x + 1 } ) ^ { 2 } - ( 1 ) ^ { 2 }$$

Evaluate

$$x$$

Solution Steps

Calculate \sqrt{x+1} to the power of 2 and get x+1.

$$x+1-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$x+1-1$$

Subtract 1 from 1 to get 0.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Calculate \sqrt{x+1} to the power of 2 and get x+1.

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

Calculate 1 to the power of 2 and get 1.

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

Subtract 1 from 1 to get 0.

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

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.

$$1$$