Solve 2x^3-8x^2x+11x-44

$$2 { x }^{ 3 } -8 { x }^{ 2 } x+11x-44$$

Evaluate

$$-6x^{3}+11x-44$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$2x^{3}-8x^{3}+11x-44$$

Combine 2x^{3} and -8x^{3} to get -6x^{3}.

$$-6x^{3}+11x-44$$

Differentiate w.r.t. x

$$11-18x^{2}$$

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}.

$$3\times 2x^{3-1}+2\left(-8x\right)x^{2-1}+11x^{1-1}$$

Multiply 3 times 2.

$$6x^{3-1}+2\left(-8x\right)x^{2-1}+11x^{1-1}$$

Subtract 1 from 3.

$$6x^{2}+2\left(-8x\right)x^{2-1}+11x^{1-1}$$

Multiply 2 times -8x.

$$6x^{2}+\left(-16x\right)x^{2-1}+11x^{1-1}$$

Subtract 1 from 2.

$$6x^{2}+\left(-16x\right)x^{1}+11x^{1-1}$$

Subtract 1 from 1.

$$6x^{2}+\left(-16x\right)x^{1}+11x^{0}$$

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

$$6x^{2}+\left(-16x\right)x+11x^{0}$$

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

$$6x^{2}+\left(-16x\right)x+11\times 1$$

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

$$6x^{2}+\left(-16x\right)x+11$$