Solve x^2-3x+2+4x^3+2x^2-1

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

Evaluate

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

Solution Steps

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

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

Subtract 1 from 2 to get 1.

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

Differentiate w.r.t. x

$$12x^{2}+6x-3$$

Steps Using Derivative Rule for Sum

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

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

Subtract 1 from 2 to get 1.

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

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}.

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

Multiply 2 times 3.

$$6x^{2-1}-3x^{1-1}+3\times 4x^{3-1}$$

Subtract 1 from 2.

$$6x^{1}-3x^{1-1}+3\times 4x^{3-1}$$

Subtract 1 from 1.

$$6x^{1}-3x^{0}+3\times 4x^{3-1}$$

Multiply 1 times -3.

$$6x^{1}-3x^{0}+12x^{3-1}$$

Subtract 1 from 3.

$$6x^{1}-3x^{0}+12x^{2}$$

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

$$6x-3x^{0}+12x^{2}$$

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

$$6x-3+12x^{2}$$