Solve 4-3a^3m-6a^2m+12am

$$4 - 3 a ^ { 3 } m - 6 a ^ { 2 } m + 12 a m$$

Differentiate w.r.t. a

$$3m\left(-a-2\right)\left(3a-2\right)$$

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}.

$$3\left(-3m\right)a^{3-1}+2\left(-6m\right)a^{2-1}+12ma^{1-1}$$

Multiply 3 times -3m.

$$\left(-9m\right)a^{3-1}+2\left(-6m\right)a^{2-1}+12ma^{1-1}$$

Subtract 1 from 3.

$$\left(-9m\right)a^{2}+2\left(-6m\right)a^{2-1}+12ma^{1-1}$$

Multiply 2 times -6m.

$$\left(-9m\right)a^{2}+\left(-12m\right)a^{2-1}+12ma^{1-1}$$

Subtract 1 from 2.

$$\left(-9m\right)a^{2}+\left(-12m\right)a^{1}+12ma^{1-1}$$

Subtract 1 from 1.

$$\left(-9m\right)a^{2}+\left(-12m\right)a^{1}+12ma^{0}$$

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

$$\left(-9m\right)a^{2}+\left(-12m\right)a+12ma^{0}$$

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

$$\left(-9m\right)a^{2}+\left(-12m\right)a+12m\times 1$$

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

$$\left(-9m\right)a^{2}+\left(-12m\right)a+12m$$

Evaluate

$$4+12am-6ma^{2}-3ma^{3}$$