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

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

Evaluate

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

Solution Steps

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

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

Subtract 3 from -5 to get -8.

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

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

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

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

Subtract 3 from -5 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-8+2x^{3}+2x)$$

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}.

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

Subtract 1 from 2.

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

Multiply 3 times 2.

$$2x^{1}+6x^{3-1}+2x^{1-1}$$

Subtract 1 from 3.

$$2x^{1}+6x^{2}+2x^{1-1}$$

Subtract 1 from 1.

$$2x^{1}+6x^{2}+2x^{0}$$

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

$$2x+6x^{2}+2x^{0}$$

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

$$2x+6x^{2}+2\times 1$$

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

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