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

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

Differentiate w.r.t. x

$$4x^{3}-10x-9$$

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}.

$$3xx^{3-1}+2\left(-5\right)x^{2-1}-9x^{1-1}$$

Subtract 1 from 3.

$$3xx^{2}+2\left(-5\right)x^{2-1}-9x^{1-1}$$

Multiply 2 times -5.

$$3xx^{2}-10x^{2-1}-9x^{1-1}$$

Subtract 1 from 2.

$$3xx^{2}-10x^{1}-9x^{1-1}$$

Subtract 1 from 1.

$$3xx^{2}-10x^{1}-9x^{0}$$

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

$$3xx^{2}-10x-9x^{0}$$

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

$$3xx^{2}-10x-9$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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