Solve xsqrt{sqrt{sqrt{sqrt{sqrt{sqrt{sqrt{sqrt{sqrt{sqrt{1}}}}}}}}}}

$$x \sqrt{ \sqrt{ \sqrt{ \sqrt{ \sqrt{ \sqrt{ \sqrt{ \sqrt{ \sqrt{ \sqrt{ 1 } } } } } } } } } }$$

Evaluate

$$x$$

Solution Steps

Calculate the square root of 1 and get 1.

$$x\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{1}}}}}}}}}$$

Calculate the square root of 1 and get 1.

$$x\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{1}}}}}}}}$$

Calculate the square root of 1 and get 1.

$$x\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{1}}}}}}}$$

Calculate the square root of 1 and get 1.

$$x\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{1}}}}}}$$

Calculate the square root of 1 and get 1.

$$x\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{1}}}}}$$

Calculate the square root of 1 and get 1.

$$x\sqrt{\sqrt{\sqrt{\sqrt{1}}}}$$

Calculate the square root of 1 and get 1.

$$x\sqrt{\sqrt{\sqrt{1}}}$$

Calculate the square root of 1 and get 1.

$$x\sqrt{\sqrt{1}}$$

Calculate the square root of 1 and get 1.

$$x\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$x\times 1$$

For any term t, t\times 1=t and 1t=t.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Calculate the square root of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{1}}}}}}}}})$$

Calculate the square root of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{1}}}}}}}})$$

Calculate the square root of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{1}}}}}}})$$

Calculate the square root of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{1}}}}}})$$

Calculate the square root of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{1}}}}})$$

Calculate the square root of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\sqrt{\sqrt{\sqrt{\sqrt{1}}}})$$

Calculate the square root of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\sqrt{\sqrt{\sqrt{1}}})$$

Calculate the square root of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\sqrt{\sqrt{1}})$$

Calculate the square root of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\sqrt{1})$$

Calculate the square root of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 1)$$

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.

$$1$$