Solve x^2+x+20+x+5

$${ x }^{ 2 } +x+20+x+5$$

Evaluate

$$x^{2}+2x+25$$

Solution Steps

Combine x and x to get 2x.

$$x^{2}+2x+20+5$$

Add 20 and 5 to get 25.

$$x^{2}+2x+25$$

Differentiate w.r.t. x

$$2\left(x+1\right)$$

Steps Using Derivative Rule for Sum

Combine x and x to get 2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+2x+20+5)$$

Add 20 and 5 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+2x+25)$$

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}.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

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

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

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

$$2x+2\times 1$$

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

$$2x+2$$