Solve 2x^2-5x+x^2+4x-3x^2-2

$$2 x ^ { 2 } - 5 x + x ^ { 2 } + 4 x - 3 x ^ { 2 } - 2$$

Evaluate

$$-x-2$$

Solution Steps

Combine 2x^{2} and x^{2} to get 3x^{2}.

$$3x^{2}-5x+4x-3x^{2}-2$$

Combine -5x and 4x to get -x.

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

Combine 3x^{2} and -3x^{2} to get 0.

$$-x-2$$

Differentiate w.r.t. x

$$-1$$

Steps Using Derivative Rule for Sum

Combine 2x^{2} and x^{2} to get 3x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}-5x+4x-3x^{2}-2)$$

Combine -5x and 4x to get -x.

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

Combine 3x^{2} and -3x^{2} to get 0.

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

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}.

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

Subtract 1 from 1.

$$-x^{0}$$

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

$$-1$$