Solve (9q+4)+(7q^2+q)

$$( 9 q + 4 ) + ( 7 q ^ { 2 } + q )$$

Differentiate w.r.t. q

$$14q+10$$

Steps Using Derivative Rule for Sum

Combine 9q and q to get 10q.

$$\frac{\mathrm{d}}{\mathrm{d}q}(10q+4+7q^{2})$$

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}.

$$10q^{1-1}+2\times 7q^{2-1}$$

Subtract 1 from 1.

$$10q^{0}+2\times 7q^{2-1}$$

Multiply 2 times 7.

$$10q^{0}+14q^{2-1}$$

Subtract 1 from 2.

$$10q^{0}+14q^{1}$$

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

$$10q^{0}+14q$$

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

$$10\times 1+14q$$

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

$$10+14q$$

Evaluate

$$7q^{2}+10q+4$$

Solution Steps

Combine 9q and q to get 10q.

$$10q+4+7q^{2}$$