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

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

Evaluate

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

Solution Steps

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

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

Combine 2x and x to get 3x.

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

Combine -2x^{2} and -2x^{2} to get -4x^{2}.

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

Differentiate w.r.t. x

$$3-8x$$

Steps Using Derivative Rule for Sum

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

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

Combine 2x and x to get 3x.

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

Combine -2x^{2} and -2x^{2} to get -4x^{2}.

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

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}.

$$2\left(-4\right)x^{2-1}+3x^{1-1}$$

Multiply 2 times -4.

$$-8x^{2-1}+3x^{1-1}$$

Subtract 1 from 2.

$$-8x^{1}+3x^{1-1}$$

Subtract 1 from 1.

$$-8x^{1}+3x^{0}$$

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

$$-8x+3x^{0}$$

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

$$-8x+3\times 1$$

For any term t, t\times 1=t and 1t=t.

$$-8x+3$$