Solve x^4-x^2+9x-1x-4

$${ x }^{ 4 } - { x }^{ 2 } +9x-1x-4$$

Differentiate w.r.t. x

$$4x^{3}-2x+8$$

Steps Using Derivative Rule for Sum

Combine 9x and -x to get 8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}-x^{2}+8x-4)$$

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}.

$$4x^{4-1}+2\left(-1\right)x^{2-1}+8x^{1-1}$$

Subtract 1 from 4.

$$4x^{3}+2\left(-1\right)x^{2-1}+8x^{1-1}$$

Multiply 2 times -1.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$4x^{3}-2x^{1}+8x^{0}$$

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

$$4x^{3}-2x+8x^{0}$$

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

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

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

$$4x^{3}-2x+8$$

Evaluate

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

Solution Steps

Combine 9x and -x to get 8x.

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