Solve 7m^2-4m+m^2+m+5

$$7 m ^ { 2 } - 4 m + m ^ { 2 } + m + 5$$

Evaluate

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

Solution Steps

Combine 7m^{2} and m^{2} to get 8m^{2}.

$$8m^{2}-4m+m+5$$

Combine -4m and m to get -3m.

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

Differentiate w.r.t. m

$$16m-3$$

Steps Using Derivative Rule for Sum

Combine 7m^{2} and m^{2} to get 8m^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(8m^{2}-4m+m+5)$$

Combine -4m and m to get -3m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(8m^{2}-3m+5)$$

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}.

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

Multiply 2 times 8.

$$16m^{2-1}-3m^{1-1}$$

Subtract 1 from 2.

$$16m^{1}-3m^{1-1}$$

Subtract 1 from 1.

$$16m^{1}-3m^{0}$$

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

$$16m-3m^{0}$$

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

$$16m-3$$