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

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

Evaluate

$$-4x^{2}+x-6$$

Solution Steps

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

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

Combine 2x and -4x to get -2x.

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

Subtract 5 from 3 to get -2.

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

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

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

Combine -2x and 3x to get x.

$$x-4x^{2}-2-4$$

Subtract 4 from -2 to get -6.

$$x-4x^{2}-6$$

Differentiate w.r.t. x

$$1-8x$$

Steps Using Derivative Rule for Sum

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

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

Combine 2x and -4x to get -2x.

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

Subtract 5 from 3 to get -2.

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

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

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

Combine -2x and 3x to get x.

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

Subtract 4 from -2 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-4x^{2}-6)$$

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}.

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

Subtract 1 from 1.

$$x^{0}+2\left(-4\right)x^{2-1}$$

Multiply 2 times -4.

$$x^{0}-8x^{2-1}$$

Subtract 1 from 2.

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

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

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

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

$$1-8x$$