Solve 2x^2+2x+2quad2x^2+x+2

$$2 x ^ { 2 } + 2 x + 2 \quad 2 x ^ { 2 } + x + 2$$

Evaluate

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

Solution Steps

Multiply 2 and 2 to get 4.

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

Combine 2x^{2} and 4x^{2} to get 6x^{2}.

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

Combine 2x and x to get 3x.

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

Differentiate w.r.t. x

$$12x+3$$

Steps Using Derivative Rule for Sum

Multiply 2 and 2 to get 4.

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

Combine 2x^{2} and 4x^{2} to get 6x^{2}.

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

Combine 2x and x to get 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2}+3x+2)$$

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}.

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

Multiply 2 times 6.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

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

$$12x+3x^{0}$$

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

$$12x+3\times 1$$

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

$$12x+3$$