Solve xsqrt{-1}xsqrt{-1}

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

Evaluate (complex solution)

$$-x^{2}$$

Solution Steps

Multiply x and x to get x^{2}.

$$x^{2}\sqrt{-1}\sqrt{-1}$$

Multiply \sqrt{-1} and \sqrt{-1} to get \left(\sqrt{-1}\right)^{2}.

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

The square of \sqrt{-1} is -1.

$$x^{2}\left(-1\right)$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Multiply x and x to get x^{2}.

$$x^{2}\sqrt{-1}\sqrt{-1}$$

Multiply \sqrt{-1} and \sqrt{-1} to get \left(\sqrt{-1}\right)^{2}.

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

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

$$x^{2}\left(-1\right)$$

Differentiate w.r.t. x

$$\text{Indeterminate}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

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

Multiply \sqrt{-1} and \sqrt{-1} to get \left(\sqrt{-1}\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\left(\sqrt{-1}\right)^{2})$$

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

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

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

$$2\left(-1\right)x^{2-1}$$

Multiply 2 times -1.

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

Subtract 1 from 2.

$$-2x^{1}$$

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

$$-2x$$