Solve 2z(-5z)=

$$2 z ( - 5 z ) =$$

Evaluate

$$-10z^{2}$$

Solution Steps

Multiply z and z to get z^{2}.

$$2z^{2}\left(-5\right)$$

Multiply 2 and -5 to get -10.

$$-10z^{2}$$

Differentiate w.r.t. z

$$-20z$$

Steps Using Definition of a Derivative

Multiply z and z to get z^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}z}(2z^{2}\left(-5\right))$$

Multiply 2 and -5 to get -10.

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

The derivative of ax^{n} is nax^{n-1}.

$$2\left(-10\right)z^{2-1}$$

Multiply 2 times -10.

$$-20z^{2-1}$$

Subtract 1 from 2.

$$-20z^{1}$$

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

$$-20z$$