Solve x+1+x*x+x*2+2*1

$$x + 1 + x \cdot x + x \cdot 2 + 2 \cdot 1$$

Evaluate

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

Solution Steps

Multiply x and x to get x^{2}.

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

Combine x and x\times 2 to get 3x.

$$3x+1+x^{2}+2\times 1$$

Multiply 2 and 1 to get 2.

$$3x+1+x^{2}+2$$

Add 1 and 2 to get 3.

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

Differentiate w.r.t. x

$$2x+3$$

Steps Using Derivative Rule for Sum

Multiply x and x to get x^{2}.

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

Combine x and x\times 2 to get 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+1+x^{2}+2\times 1)$$

Multiply 2 and 1 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+1+x^{2}+2)$$

Add 1 and 2 to get 3.

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

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}.

$$3x^{1-1}+2x^{2-1}$$

Subtract 1 from 1.

$$3x^{0}+2x^{2-1}$$

Subtract 1 from 2.

$$3x^{0}+2x^{1}$$

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

$$3x^{0}+2x$$

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

$$3\times 1+2x$$

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

$$3+2x$$