Solve x^5-6x^2+9x-3

$${ x }^{ 5 } -6 { x }^{ 2 } +9x-3$$

Differentiate w.r.t. x

$$5x^{4}-12x+9$$

Steps Using Derivative Rule for Sum

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}.

$$5x^{5-1}+2\left(-6\right)x^{2-1}+9x^{1-1}$$

Subtract 1 from 5.

$$5x^{4}+2\left(-6\right)x^{2-1}+9x^{1-1}$$

Multiply 2 times -6.

$$5x^{4}-12x^{2-1}+9x^{1-1}$$

Subtract 1 from 2.

$$5x^{4}-12x^{1}+9x^{1-1}$$

Subtract 1 from 1.

$$5x^{4}-12x^{1}+9x^{0}$$

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

$$5x^{4}-12x+9x^{0}$$

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

$$5x^{4}-12x+9\times 1$$

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

$$5x^{4}-12x+9$$

Evaluate

$$x^{5}-6x^{2}+9x-3$$