Solve 1/x-1-1

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

Differentiate w.r.t. x

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

Steps Using Chain Rule

Subtract 1 from -1 to get -2.

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

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

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

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}.

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

Simplify.

$$-x^{0}\left(x^{1}-2\right)^{-2}$$

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

$$-x^{0}\left(x-2\right)^{-2}$$

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

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

Evaluate

$$\frac{1}{x-2}$$

Solution Steps

Subtract 1 from -1 to get -2.

$$\frac{1}{x-2}$$