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

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

Differentiate w.r.t. x

$$-24x^{2}+18x-2$$

Steps Using Derivative Rule for Sum

Combine x^{2} and 8x^{2} to get 9x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{2}-8x^{3}-2x-8)$$

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}.

$$2\times 9x^{2-1}+3\left(-8\right)x^{3-1}-2x^{1-1}$$

Multiply 2 times 9.

$$18x^{2-1}+3\left(-8\right)x^{3-1}-2x^{1-1}$$

Subtract 1 from 2.

$$18x^{1}+3\left(-8\right)x^{3-1}-2x^{1-1}$$

Multiply 3 times -8.

$$18x^{1}-24x^{3-1}-2x^{1-1}$$

Subtract 1 from 3.

$$18x^{1}-24x^{2}-2x^{1-1}$$

Subtract 1 from 1.

$$18x^{1}-24x^{2}-2x^{0}$$

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

$$18x-24x^{2}-2x^{0}$$

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

$$18x-24x^{2}-2$$

Evaluate

$$-8x^{3}+9x^{2}-2x-8$$

Solution Steps

Combine x^{2} and 8x^{2} to get 9x^{2}.

$$9x^{2}-8x^{3}-2x-8$$