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

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

Differentiate w.r.t. m

$$9m^{2}+10m+5$$

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}.

$$3\times 3m^{3-1}+2\times 5m^{2-1}+5m^{1-1}$$

Multiply 3 times 3.

$$9m^{3-1}+2\times 5m^{2-1}+5m^{1-1}$$

Subtract 1 from 3.

$$9m^{2}+2\times 5m^{2-1}+5m^{1-1}$$

Multiply 2 times 5.

$$9m^{2}+10m^{2-1}+5m^{1-1}$$

Subtract 1 from 2.

$$9m^{2}+10m^{1}+5m^{1-1}$$

Subtract 1 from 1.

$$9m^{2}+10m^{1}+5m^{0}$$

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

$$9m^{2}+10m+5m^{0}$$

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

$$9m^{2}+10m+5\times 1$$

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

$$9m^{2}+10m+5$$

Evaluate

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