Solve 2m+(3m^2+5m+6)

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

Differentiate w.r.t. m

$$6m+7$$

Steps Using Derivative Rule for Sum

Combine 2m and 5m to get 7m.

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

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}.

$$7m^{1-1}+2\times 3m^{2-1}$$

Subtract 1 from 1.

$$7m^{0}+2\times 3m^{2-1}$$

Multiply 2 times 3.

$$7m^{0}+6m^{2-1}$$

Subtract 1 from 2.

$$7m^{0}+6m^{1}$$

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

$$7m^{0}+6m$$

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

$$7\times 1+6m$$

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

$$7+6m$$

Evaluate

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

Solution Steps

Combine 2m and 5m to get 7m.

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