Solve 2x^2-3x+2-x^2+4x+1=

$$2 x ^ { 2 } - 3 x + 2 - x ^ { 2 } + 4 x + 1 =$$

Evaluate

$$x^{2}+x+3$$

Solution Steps

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

$$x^{2}-3x+2+4x+1$$

Combine -3x and 4x to get x.

$$x^{2}+x+2+1$$

Add 2 and 1 to get 3.

$$x^{2}+x+3$$

Differentiate w.r.t. x

$$2x+1$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-3x+2+4x+1)$$

Combine -3x and 4x to get x.

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

Add 2 and 1 to get 3.

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

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.

$$2x+1$$