Solve (2x+3)+(x^2-1)*(1)

$$(2x+3)+( { x }^{ 2 } -1) \times (1)$$

Evaluate

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

Solution Steps

Use the distributive property to multiply x^{2}-1 by 1.

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

Subtract 1 from 3 to get 2.

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

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

Use the distributive property to multiply x^{2}-1 by 1.

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

Subtract 1 from 3 to get 2.

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

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}.

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

Subtract 1 from 1.

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

Subtract 1 from 2.

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

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

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

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

$$2\times 1+2x$$

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

$$2+2x$$