Solve x^3-10x^2+23x-14+x+2

$$x ^ { 3 } - 10 x ^ { 2 } + 23 x - 14 + x + 2$$

Evaluate

$$x^{3}-10x^{2}+24x-12$$

Solution Steps

Combine 23x and x to get 24x.

$$x^{3}-10x^{2}+24x-14+2$$

Add -14 and 2 to get -12.

$$x^{3}-10x^{2}+24x-12$$

Differentiate w.r.t. x

$$3x^{2}-20x+24$$

Steps Using Derivative Rule for Sum

Combine 23x and x to get 24x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}-10x^{2}+24x-14+2)$$

Add -14 and 2 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}-10x^{2}+24x-12)$$

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}.

$$3x^{3-1}+2\left(-10\right)x^{2-1}+24x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\left(-10\right)x^{2-1}+24x^{1-1}$$

Multiply 2 times -10.

$$3x^{2}-20x^{2-1}+24x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}-20x^{1}+24x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}-20x^{1}+24x^{0}$$

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

$$3x^{2}-20x+24x^{0}$$

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

$$3x^{2}-20x+24\times 1$$

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

$$3x^{2}-20x+24$$