Solve 3z^2-2z+5-z^2+z-1

$$3 { z }^{ 2 } -2z+5- { z }^{ 2 } +z-1$$

Evaluate

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

Solution Steps

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

$$2z^{2}-2z+5+z-1$$

Combine -2z and z to get -z.

$$2z^{2}-z+5-1$$

Subtract 1 from 5 to get 4.

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

Differentiate w.r.t. z

$$4z-1$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}z}(2z^{2}-2z+5+z-1)$$

Combine -2z and z to get -z.

$$\frac{\mathrm{d}}{\mathrm{d}z}(2z^{2}-z+5-1)$$

Subtract 1 from 5 to get 4.

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

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}.

$$2\times 2z^{2-1}-z^{1-1}$$

Multiply 2 times 2.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$4z^{1}-z^{0}$$

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

$$4z-z^{0}$$

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

$$4z-1$$