Solve 25-9m^2-m+4m^3

$$25 - 9 m ^ { 2 } - m + 4 m ^ { 3 }$$

Differentiate w.r.t. m

$$12m^{2}-18m-1$$

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}.

$$2\left(-9\right)m^{2-1}-m^{1-1}+3\times 4m^{3-1}$$

Multiply 2 times -9.

$$-18m^{2-1}-m^{1-1}+3\times 4m^{3-1}$$

Subtract 1 from 2.

$$-18m^{1}-m^{1-1}+3\times 4m^{3-1}$$

Subtract 1 from 1.

$$-18m^{1}-m^{0}+3\times 4m^{3-1}$$

Multiply 1 times -1.

$$-18m^{1}-m^{0}+12m^{3-1}$$

Subtract 1 from 3.

$$-18m^{1}-m^{0}+12m^{2}$$

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

$$-18m-m^{0}+12m^{2}$$

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

$$-18m-1+12m^{2}$$

Evaluate

$$4m^{3}-9m^{2}-m+25$$