Solve f(x)=1-36x-21x^2-2x^3

$$f ( x ) = 1 - 36 x - 21 x ^ { 2 } - 2 x ^ { 3 }$$

Differentiate w.r.t. x

$$6\left(-x-1\right)\left(x+6\right)$$

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}.

$$-36x^{1-1}+2\left(-21\right)x^{2-1}+3\left(-2\right)x^{3-1}$$

Subtract 1 from 1.

$$-36x^{0}+2\left(-21\right)x^{2-1}+3\left(-2\right)x^{3-1}$$

Multiply 2 times -21.

$$-36x^{0}-42x^{2-1}+3\left(-2\right)x^{3-1}$$

Subtract 1 from 2.

$$-36x^{0}-42x^{1}+3\left(-2\right)x^{3-1}$$

Multiply 2 times -21.

$$-36x^{0}-42x^{1}-6x^{3-1}$$

Subtract 1 from 3.

$$-36x^{0}-42x^{1}-6x^{2}$$

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

$$-36x^{0}-42x-6x^{2}$$

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

$$-36-42x-6x^{2}$$

Evaluate

$$1-36x-21x^{2}-2x^{3}$$