Solve (2x+1+x^2-3x)

$$( 2 x + 1 + x ^ { 2 } - 3 x )$$

Differentiate w.r.t. x

$$2x-1$$

Steps Using Derivative Rule for Sum

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

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

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}.

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

Subtract 1 from 1.

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

Subtract 1 from 2.

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

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

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

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

$$-1+2x$$

Evaluate

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

Solution Steps

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

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