Solve (8z^2+7z)+(3z^2+6)

$$( 8 z ^ { 2 } + 7 z ) + ( 3 z ^ { 2 } + 6 )$$

Differentiate w.r.t. z

$$22z+7$$

Steps Using Derivative Rule for Sum

Combine 8z^{2} and 3z^{2} to get 11z^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}z}(11z^{2}+7z+6)$$

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}.

$$2\times 11z^{2-1}+7z^{1-1}$$

Multiply 2 times 11.

$$22z^{2-1}+7z^{1-1}$$

Subtract 1 from 2.

$$22z^{1}+7z^{1-1}$$

Subtract 1 from 1.

$$22z^{1}+7z^{0}$$

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

$$22z+7z^{0}$$

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

$$22z+7\times 1$$

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

$$22z+7$$

Evaluate

$$11z^{2}+7z+6$$

Solution Steps

Combine 8z^{2} and 3z^{2} to get 11z^{2}.

$$11z^{2}+7z+6$$