Solve z^2+10z+24quad2

$$z ^ { 2 } + 10 z + 24 \quad 2$$

Differentiate w.r.t. z

$$2\left(z+5\right)$$

Steps Using Derivative Rule for Sum

Multiply 24 and 2 to get 48.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{2}+10z+48)$$

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}.

$$2z^{2-1}+10z^{1-1}$$

Subtract 1 from 2.

$$2z^{1}+10z^{1-1}$$

Subtract 1 from 1.

$$2z^{1}+10z^{0}$$

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

$$2z+10z^{0}$$

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

$$2z+10\times 1$$

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

$$2z+10$$

Evaluate

$$z^{2}+10z+48$$

Solution Steps

Multiply 24 and 2 to get 48.

$$z^{2}+10z+48$$