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

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

Evaluate

$$3-x^{2}$$

Solution Steps

Combine x^{2} and -x^{2} to get 0.

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

Combine -2x and 2x to get 0.

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

Differentiate w.r.t. x

$$-2x$$

Steps Using Derivative Rule for Sum

Combine x^{2} and -x^{2} to get 0.

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

Combine -2x and 2x to get 0.

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

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}.

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

Multiply 2 times -1.

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

Subtract 1 from 2.

$$-2x^{1}$$

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

$$-2x$$