Solve x^22x^3-13x^2-14x+24

$${ x }^{ 2 } 2 { x }^{ 3 } -13 { x }^{ 2 } -14x+24$$

Differentiate w.r.t. x

$$10x^{4}-26x-14$$

Steps Using Derivative Rule for Sum

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}\times 2-13x^{2}-14x+24)$$

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}.

$$5\times 2x^{5-1}+2\left(-13\right)x^{2-1}-14x^{1-1}$$

Multiply 5 times 2.

$$10x^{5-1}+2\left(-13\right)x^{2-1}-14x^{1-1}$$

Subtract 1 from 5.

$$10x^{4}+2\left(-13\right)x^{2-1}-14x^{1-1}$$

Multiply 2 times -13.

$$10x^{4}-26x^{2-1}-14x^{1-1}$$

Subtract 1 from 2.

$$10x^{4}-26x^{1}-14x^{1-1}$$

Subtract 1 from 1.

$$10x^{4}-26x^{1}-14x^{0}$$

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

$$10x^{4}-26x-14x^{0}$$

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

$$10x^{4}-26x-14$$

Evaluate

$$2x^{5}-13x^{2}-14x+24$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$x^{5}\times 2-13x^{2}-14x+24$$