Solve 3z^2+2z-12z^2-8

$$3 z ^ { 2 } + 2 z - 12 z ^ { 2 } - 8$$

Differentiate w.r.t. z

$$2-18z$$

Steps Using Derivative Rule for Sum

Combine 3z^{2} and -12z^{2} to get -9z^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-9z^{2}+2z-8)$$

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}.

$$2\left(-9\right)z^{2-1}+2z^{1-1}$$

Multiply 2 times -9.

$$-18z^{2-1}+2z^{1-1}$$

Subtract 1 from 2.

$$-18z^{1}+2z^{1-1}$$

Subtract 1 from 1.

$$-18z^{1}+2z^{0}$$

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

$$-18z+2z^{0}$$

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

$$-18z+2\times 1$$

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

$$-18z+2$$

Evaluate

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

Solution Steps

Combine 3z^{2} and -12z^{2} to get -9z^{2}.

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