Solve (x^3-9x^2+21x+2)+(x-4)

$$( x ^ { 3 } - 9 x ^ { 2 } + 21 x + 2 ) + ( x - 4 )$$

Evaluate

$$x^{3}-9x^{2}+22x-2$$

Solution Steps

Combine 21x and x to get 22x.

$$x^{3}-9x^{2}+22x+2-4$$

Subtract 4 from 2 to get -2.

$$x^{3}-9x^{2}+22x-2$$

Differentiate w.r.t. x

$$3x^{2}-18x+22$$

Steps Using Derivative Rule for Sum

Combine 21x and x to get 22x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}-9x^{2}+22x+2-4)$$

Subtract 4 from 2 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}-9x^{2}+22x-2)$$

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}.

$$3x^{3-1}+2\left(-9\right)x^{2-1}+22x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\left(-9\right)x^{2-1}+22x^{1-1}$$

Multiply 2 times -9.

$$3x^{2}-18x^{2-1}+22x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}-18x^{1}+22x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}-18x^{1}+22x^{0}$$

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

$$3x^{2}-18x+22x^{0}$$

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

$$3x^{2}-18x+22\times 1$$

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

$$3x^{2}-18x+22$$