Solve -2z+-7z+6z+-7z

$$- 2 z + - 7 z + 6 z + - 7 z$$

Evaluate

$$-10z$$

Solution Steps

Combine -2z and -7z to get -9z.

$$-9z+6z-7z$$

Combine -9z and 6z to get -3z.

$$-3z-7z$$

Combine -3z and -7z to get -10z.

$$-10z$$

Differentiate w.r.t. z

$$-10$$

Steps Using Definition of a Derivative

Combine -2z and -7z to get -9z.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-9z+6z-7z)$$

Combine -9z and 6z to get -3z.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-3z-7z)$$

Combine -3z and -7z to get -10z.

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

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

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

Subtract 1 from 1.

$$-10z^{0}$$

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

$$-10$$