Solve 2x^2-3x+10-x^2+2x+8

$$2 x ^ { 2 } - 3 x + 10 - x ^ { 2 } + 2 x + 8$$

Evaluate

$$x^{2}-x+18$$

Solution Steps

Combine 2x^{2} and -x^{2} to get x^{2}.

$$x^{2}-3x+10+2x+8$$

Combine -3x and 2x to get -x.

$$x^{2}-x+10+8$$

Add 10 and 8 to get 18.

$$x^{2}-x+18$$

Differentiate w.r.t. x

$$2x-1$$

Steps Using Derivative Rule for Sum

Combine 2x^{2} and -x^{2} to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-3x+10+2x+8)$$

Combine -3x and 2x to get -x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x+10+8)$$

Add 10 and 8 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x+18)$$

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.

$$2x-1$$