Solve (4x^2+2x+1)+(3x^2+4x+1)

$$( 4 x ^ { 2 } + 2 x + 1 ) + ( 3 x ^ { 2 } + 4 x + 1 )$$

Evaluate

$$7x^{2}+6x+2$$

Solution Steps

Combine 4x^{2} and 3x^{2} to get 7x^{2}.

$$7x^{2}+2x+1+4x+1$$

Combine 2x and 4x to get 6x.

$$7x^{2}+6x+1+1$$

Add 1 and 1 to get 2.

$$7x^{2}+6x+2$$

Differentiate w.r.t. x

$$14x+6$$

Steps Using Derivative Rule for Sum

Combine 4x^{2} and 3x^{2} to get 7x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}+2x+1+4x+1)$$

Combine 2x and 4x to get 6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}+6x+1+1)$$

Add 1 and 1 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}+6x+2)$$

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}.

$$2\times 7x^{2-1}+6x^{1-1}$$

Multiply 2 times 7.

$$14x^{2-1}+6x^{1-1}$$

Subtract 1 from 2.

$$14x^{1}+6x^{1-1}$$

Subtract 1 from 1.

$$14x^{1}+6x^{0}$$

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

$$14x+6x^{0}$$

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

$$14x+6\times 1$$

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

$$14x+6$$