Solve (1-2a-4a^2-8a^3

$$(1-2a-4 { a }^{ 2 } -8 { a }^{ 3 }$$

Differentiate w.r.t. a

$$-24a^{2}-8a-2$$

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}.

$$-2a^{1-1}+2\left(-4\right)a^{2-1}+3\left(-8\right)a^{3-1}$$

Subtract 1 from 1.

$$-2a^{0}+2\left(-4\right)a^{2-1}+3\left(-8\right)a^{3-1}$$

Multiply 2 times -4.

$$-2a^{0}-8a^{2-1}+3\left(-8\right)a^{3-1}$$

Subtract 1 from 2.

$$-2a^{0}-8a^{1}+3\left(-8\right)a^{3-1}$$

Multiply 2 times -4.

$$-2a^{0}-8a^{1}-24a^{3-1}$$

Subtract 1 from 3.

$$-2a^{0}-8a^{1}-24a^{2}$$

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

$$-2a^{0}-8a-24a^{2}$$

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

$$-2-8a-24a^{2}$$

Evaluate

$$1-2a-4a^{2}-8a^{3}$$