Solve =m^3-2m-3m^2+12text{para}m=-2

$$= m ^ { 3 } - 2 m - 3 m ^ { 2 } + 12 \text { para } m = - 2$$

Differentiate w.r.t. m

$$3m^{2}-6m-2$$

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}.

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

Subtract 1 from 3.

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

Subtract 1 from 1.

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

Multiply 1 times -2.

$$3m^{2}-2m^{0}-6m^{2-1}$$

Subtract 1 from 2.

$$3m^{2}-2m^{0}-6m^{1}$$

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

$$3m^{2}-2m^{0}-6m$$

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

$$3m^{2}-2-6m$$

Evaluate

$$m^{3}-3m^{2}-2m+12$$