Solve -4+2z^2-5z+8+z^2+9z

$$- 4 + 2 z ^ { 2 } - 5 z + 8 + z ^ { 2 } + 9 z$$

Evaluate

$$3z^{2}+4z+4$$

Solution Steps

Add -4 and 8 to get 4.

$$4+2z^{2}-5z+z^{2}+9z$$

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

$$4+3z^{2}-5z+9z$$

Combine -5z and 9z to get 4z.

$$4+3z^{2}+4z$$

Differentiate w.r.t. z

$$6z+4$$

Steps Using Derivative Rule for Sum

Add -4 and 8 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}z}(4+2z^{2}-5z+z^{2}+9z)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}z}(4+3z^{2}-5z+9z)$$

Combine -5z and 9z to get 4z.

$$\frac{\mathrm{d}}{\mathrm{d}z}(4+3z^{2}+4z)$$

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}.

$$2\times 3z^{2-1}+4z^{1-1}$$

Multiply 2 times 3.

$$6z^{2-1}+4z^{1-1}$$

Subtract 1 from 2.

$$6z^{1}+4z^{1-1}$$

Subtract 1 from 1.

$$6z^{1}+4z^{0}$$

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

$$6z+4z^{0}$$

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

$$6z+4\times 1$$

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

$$6z+4$$