Solve (x-1)x(x-2)^0

$$( x - 1 ) x ( x - 2 ) ^ { 0 }$$

Evaluate

$$x\left(x-1\right)$$

Solution Steps

Calculate x-2 to the power of 0 and get 1.

$$\left(x-1\right)x\times 1$$

Use the distributive property to multiply x-1 by x.

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

Use the distributive property to multiply x^{2}-x by 1.

$$x^{2}-x$$

Differentiate w.r.t. x

$$2x-1$$

Steps Using Derivative Rule for Sum

Calculate x-2 to the power of 0 and get 1.

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

Use the distributive property to multiply x-1 by x.

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

Use the distributive property to multiply x^{2}-x by 1.

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

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}.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$2x^{1}-x^{0}$$

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

$$2x-x^{0}$$

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

$$2x-1$$