Solve x^2+1+6x^2+7x-2=

$${ x }^{ 2+1 } +6 { x }^{ 2 } +7x-2=$$

Differentiate w.r.t. x

$$3x^{2}+12x+7$$

Steps Using Derivative Rule for Sum

Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}+6x^{2}+7x-2)$$

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}.

$$3x^{3-1}+2\times 6x^{2-1}+7x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\times 6x^{2-1}+7x^{1-1}$$

Multiply 2 times 6.

$$3x^{2}+12x^{2-1}+7x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}+12x^{1}+7x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}+12x^{1}+7x^{0}$$

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

$$3x^{2}+12x+7x^{0}$$

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

$$3x^{2}+12x+7\times 1$$

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

$$3x^{2}+12x+7$$

Evaluate

$$\left(x+2\right)\left(x^{2}+4x-1\right)$$

Solution Steps

Add 2 and 1 to get 3.

$$x^{3}+6x^{2}+7x-2$$