Solve 9x^2-6x^3-2x^2+16x+8

$$9 x ^ { 2 } - 6 x ^ { 3 } - 2 x ^ { 2 } + 16 x + 8$$

Differentiate w.r.t. x

$$16+14x-18x^{2}$$

Steps Using Derivative Rule for Sum

Combine 9x^{2} and -2x^{2} to get 7x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}-6x^{3}+16x+8)$$

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}.

$$2\times 7x^{2-1}+3\left(-6\right)x^{3-1}+16x^{1-1}$$

Multiply 2 times 7.

$$14x^{2-1}+3\left(-6\right)x^{3-1}+16x^{1-1}$$

Subtract 1 from 2.

$$14x^{1}+3\left(-6\right)x^{3-1}+16x^{1-1}$$

Multiply 3 times -6.

$$14x^{1}-18x^{3-1}+16x^{1-1}$$

Subtract 1 from 3.

$$14x^{1}-18x^{2}+16x^{1-1}$$

Subtract 1 from 1.

$$14x^{1}-18x^{2}+16x^{0}$$

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

$$14x-18x^{2}+16x^{0}$$

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

$$14x-18x^{2}+16\times 1$$

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

$$14x-18x^{2}+16$$

Evaluate

$$8+16x+7x^{2}-6x^{3}$$

Solution Steps

Combine 9x^{2} and -2x^{2} to get 7x^{2}.

$$7x^{2}-6x^{3}+16x+8$$