Solve (5x^2+3x+6)+(7x^2-2x+3)

$$(5 { x }^{ 2 } +3x+6)+(7 { x }^{ 2 } -2x+3)$$

Evaluate

$$12x^{2}+x+9$$

Solution Steps

Combine 5x^{2} and 7x^{2} to get 12x^{2}.

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

Combine 3x and -2x to get x.

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

Add 6 and 3 to get 9.

$$12x^{2}+x+9$$

Differentiate w.r.t. x

$$24x+1$$

Steps Using Derivative Rule for Sum

Combine 5x^{2} and 7x^{2} to get 12x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{2}+3x+6-2x+3)$$

Combine 3x and -2x to get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{2}+x+6+3)$$

Add 6 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{2}+x+9)$$

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}.

$$2\times 12x^{2-1}+x^{1-1}$$

Multiply 2 times 12.

$$24x^{2-1}+x^{1-1}$$

Subtract 1 from 2.

$$24x^{1}+x^{1-1}$$

Subtract 1 from 1.

$$24x^{1}+x^{0}$$

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

$$24x+x^{0}$$

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

$$24x+1$$