Solve 9m^3-3m^2+8m-5

$$9 m ^ { 3 } - 3 m ^ { 2 } + 8 m - 5$$

Differentiate w.r.t. m

$$27m^{2}-6m+8$$

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}.

$$3\times 9m^{3-1}+2\left(-3\right)m^{2-1}+8m^{1-1}$$

Multiply 3 times 9.

$$27m^{3-1}+2\left(-3\right)m^{2-1}+8m^{1-1}$$

Subtract 1 from 3.

$$27m^{2}+2\left(-3\right)m^{2-1}+8m^{1-1}$$

Multiply 2 times -3.

$$27m^{2}-6m^{2-1}+8m^{1-1}$$

Subtract 1 from 2.

$$27m^{2}-6m^{1}+8m^{1-1}$$

Subtract 1 from 1.

$$27m^{2}-6m^{1}+8m^{0}$$

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

$$27m^{2}-6m+8m^{0}$$

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

$$27m^{2}-6m+8\times 1$$

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

$$27m^{2}-6m+8$$

Evaluate

$$9m^{3}-3m^{2}+8m-5$$