Solve 1+2a-3a^2-6a^3quad(3

$$1 + 2 a - 3 a ^ { 2 } - 6 a ^ { 3 } \quad (3$$

Differentiate w.r.t. a

$$2-6a-54a^{2}$$

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}.

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

Subtract 1 from 1.

$$2a^{0}+2\left(-3\right)a^{2-1}+3\left(-18\right)a^{3-1}$$

Multiply 2 times -3.

$$2a^{0}-6a^{2-1}+3\left(-18\right)a^{3-1}$$

Subtract 1 from 2.

$$2a^{0}-6a^{1}+3\left(-18\right)a^{3-1}$$

Multiply 2 times -3.

$$2a^{0}-6a^{1}-54a^{3-1}$$

Subtract 1 from 3.

$$2a^{0}-6a^{1}-54a^{2}$$

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

$$2a^{0}-6a-54a^{2}$$

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

$$2\times 1-6a-54a^{2}$$

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

$$2-6a-54a^{2}$$

Evaluate

$$1+2a-3a^{2}-18a^{3}$$

Solution Steps

Multiply 6 and 3 to get 18.

$$1+2a-3a^{2}-18a^{3}$$