Solve 1/frac{1{(x-1)-1}}

$$\frac{ 1 }{ \frac{ 1 }{ (x-1)-1 } }$$

Evaluate

$$x-2$$

Solution Steps

Divide 1 by \frac{1}{x-1-1} by multiplying 1 by the reciprocal of \frac{1}{x-1-1}.

$$x-1-1$$

Subtract 1 from -1 to get -2.

$$x-2$$

Combine x and x to get 2x.

$$2x-2$$

Differentiate w.r.t. x

$$1$$

Steps Using Derivative Rule for Sum

Divide 1 by \frac{1}{x-1-1} by multiplying 1 by the reciprocal of \frac{1}{x-1-1}.

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

Subtract 1 from -1 to get -2.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. 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.

$$1$$