Solve x+4x^22+6x+8

$$x+4 { x }^{ 2 } 2+6x+8$$

Evaluate

$$8x^{2}+7x+8$$

Solution Steps

Multiply 4 and 2 to get 8.

$$x+8x^{2}+6x+8$$

Combine x and 6x to get 7x.

$$7x+8x^{2}+8$$

Differentiate w.r.t. x

$$16x+7$$

Steps Using Derivative Rule for Sum

Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+8x^{2}+6x+8)$$

Combine x and 6x to get 7x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x+8x^{2}+8)$$

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}.

$$7x^{1-1}+2\times 8x^{2-1}$$

Subtract 1 from 1.

$$7x^{0}+2\times 8x^{2-1}$$

Multiply 2 times 8.

$$7x^{0}+16x^{2-1}$$

Subtract 1 from 2.

$$7x^{0}+16x^{1}$$

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

$$7x^{0}+16x$$

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

$$7\times 1+16x$$

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

$$7+16x$$