Solve x^4+2x-3x^2divx^2-1

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

Evaluate

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

Solution Steps

Cancel out x^{2} in both numerator and denominator.

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

Subtract 1 from -3 to get -4.

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

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

Cancel out x^{2} in both numerator and denominator.

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

Subtract 1 from -3 to get -4.

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

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}.

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

Subtract 1 from 4.

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

Subtract 1 from 1.

$$4x^{3}+2x^{0}$$

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

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

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

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