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

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

Evaluate

$$2x$$

Solution Steps

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

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

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

$$x+1+x-1$$

Combine x and x to get 2x.

$$2x+1-1$$

Subtract 1 from 1 to get 0.

$$2x$$

Differentiate w.r.t. x

$$2$$

Steps Using Definition of a Derivative

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

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

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

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

Combine x and x to get 2x.

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

Subtract 1 from 1 to get 0.

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

The derivative of ax^{n} is nax^{n-1}.

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

Subtract 1 from 1.

$$2x^{0}$$

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

$$2\times 1$$

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

$$2$$