Solve 6-x+x^2+2x

$$6-x+ { x }^{ 2 } +2x$$

Differentiate w.r.t. x

$$2x+1$$

Steps Using Derivative Rule for Sum

Combine -x and 2x to get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6+x+x^{2})$$

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

$$x^{2}+x+6$$

Solution Steps

Combine -x and 2x to get x.

$$6+x+x^{2}$$