Solve (8m^3+6m^2+5m)+(-8m-7)

$$( 8 m ^ { 3 } + 6 m ^ { 2 } + 5 m ) + ( - 8 m - 7 )$$

Differentiate w.r.t. m

$$24m^{2}+12m-3$$

Steps Using Derivative Rule for Sum

Combine 5m and -8m to get -3m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(8m^{3}+6m^{2}-3m-7)$$

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}.

$$3\times 8m^{3-1}+2\times 6m^{2-1}-3m^{1-1}$$

Multiply 3 times 8.

$$24m^{3-1}+2\times 6m^{2-1}-3m^{1-1}$$

Subtract 1 from 3.

$$24m^{2}+2\times 6m^{2-1}-3m^{1-1}$$

Multiply 2 times 6.

$$24m^{2}+12m^{2-1}-3m^{1-1}$$

Subtract 1 from 2.

$$24m^{2}+12m^{1}-3m^{1-1}$$

Subtract 1 from 1.

$$24m^{2}+12m^{1}-3m^{0}$$

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

$$24m^{2}+12m-3m^{0}$$

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

$$24m^{2}+12m-3$$

Evaluate

$$8m^{3}+6m^{2}-3m-7$$

Solution Steps

Combine 5m and -8m to get -3m.

$$8m^{3}+6m^{2}-3m-7$$