Solve x^2+4x+4+4x+80

$$x ^ { 2 } + 4 x + 4 + 4 x + 80$$

Evaluate

$$x^{2}+8x+84$$

Solution Steps

Combine 4x and 4x to get 8x.

$$x^{2}+8x+4+80$$

Add 4 and 80 to get 84.

$$x^{2}+8x+84$$

Differentiate w.r.t. x

$$2\left(x+4\right)$$

Steps Using Derivative Rule for Sum

Combine 4x and 4x to get 8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+8x+4+80)$$

Add 4 and 80 to get 84.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+8x+84)$$

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}.

$$2x^{2-1}+8x^{1-1}$$

Subtract 1 from 2.

$$2x^{1}+8x^{1-1}$$

Subtract 1 from 1.

$$2x^{1}+8x^{0}$$

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

$$2x+8x^{0}$$

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

$$2x+8\times 1$$

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

$$2x+8$$