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

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

Evaluate

$$2x^{3}+3x+7$$

Solution Steps

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

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

Combine -x and 4x to get 3x.

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

Add 2 and 5 to get 7.

$$2x^{3}+3x+7$$

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

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

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

Combine -x and 4x to get 3x.

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

Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+3x+7)$$

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}.

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

Multiply 3 times 2.

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

Subtract 1 from 3.

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

Subtract 1 from 1.

$$6x^{2}+3x^{0}$$

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

$$6x^{2}+3\times 1$$

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

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