Solve (x^2-x+2)+(4x^2+7x+2))=4x^2

$$( x ^ { 2 } - x + 2 ) + ( 4 x ^ { 2 } + 7 x + 2 ) ) = 4 x ^ { 2 }$$

Evaluate

$$5x^{2}+6x+4$$

Solution Steps

Combine x^{2} and 4x^{2} to get 5x^{2}.

$$5x^{2}-x+2+7x+2$$

Combine -x and 7x to get 6x.

$$5x^{2}+6x+2+2$$

Add 2 and 2 to get 4.

$$5x^{2}+6x+4$$

Differentiate w.r.t. x

$$10x+6$$

Steps Using Derivative Rule for Sum

Combine x^{2} and 4x^{2} to get 5x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}-x+2+7x+2)$$

Combine -x and 7x to get 6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}+6x+2+2)$$

Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}+6x+4)$$

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}.

$$2\times 5x^{2-1}+6x^{1-1}$$

Multiply 2 times 5.

$$10x^{2-1}+6x^{1-1}$$

Subtract 1 from 2.

$$10x^{1}+6x^{1-1}$$

Subtract 1 from 1.

$$10x^{1}+6x^{0}$$

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

$$10x+6x^{0}$$

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

$$10x+6\times 1$$

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

$$10x+6$$