Solve =2x^4+4x^2+2-x^2+1

$$= 2 x ^ { 4 } + 4 x ^ { 2 } + 2 - x ^ { 2 } + 1$$

Evaluate

$$2x^{4}+3x^{2}+3$$

Solution Steps

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$2x^{4}+3x^{2}+2+1$$

Add 2 and 1 to get 3.

$$2x^{4}+3x^{2}+3$$

Differentiate w.r.t. x

$$8x^{3}+6x$$

Steps Using Derivative Rule for Sum

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}+3x^{2}+2+1)$$

Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}+3x^{2}+3)$$

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}.

$$4\times 2x^{4-1}+2\times 3x^{2-1}$$

Multiply 4 times 2.

$$8x^{4-1}+2\times 3x^{2-1}$$

Subtract 1 from 4.

$$8x^{3}+2\times 3x^{2-1}$$

Multiply 2 times 3.

$$8x^{3}+6x^{2-1}$$

Subtract 1 from 2.

$$8x^{3}+6x^{1}$$

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

$$8x^{3}+6x$$