Solve f(x)=16-13x-20x^2-2x^3

$$f ( x ) = 16 - 13 x - 20 x ^ { 2 } - 2 x ^ { 3 }$$

Differentiate w.r.t. x

$$-6x^{2}-40x-13$$

Steps Using Derivative Rule for Sum

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}.

$$-13x^{1-1}+2\left(-20\right)x^{2-1}+3\left(-2\right)x^{3-1}$$

Subtract 1 from 1.

$$-13x^{0}+2\left(-20\right)x^{2-1}+3\left(-2\right)x^{3-1}$$

Multiply 2 times -20.

$$-13x^{0}-40x^{2-1}+3\left(-2\right)x^{3-1}$$

Subtract 1 from 2.

$$-13x^{0}-40x^{1}+3\left(-2\right)x^{3-1}$$

Multiply 2 times -20.

$$-13x^{0}-40x^{1}-6x^{3-1}$$

Subtract 1 from 3.

$$-13x^{0}-40x^{1}-6x^{2}$$

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

$$-13x^{0}-40x-6x^{2}$$

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

$$-13-40x-6x^{2}$$

Evaluate

$$16-13x-20x^{2}-2x^{3}$$