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

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

Evaluate

$$x^{4}+3$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

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

Combine -2x^{2} and 2x^{2} to get 0.

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

Add 1 and 2 to get 3.

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

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

$$3+x^{4}$$

Differentiate w.r.t. x

$$4x^{3}$$

Steps Using Derivative Rule for Sum

Calculate 1 to the power of 2 and get 1.

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

Combine -2x^{2} and 2x^{2} to get 0.

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

Add 1 and 2 to get 3.

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

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}.

$$4x^{4-1}$$

Subtract 1 from 4.

$$4x^{3}$$