Solve -81x+19y-30z+6y+80x+x-25y

$$-81x+19y-30z+6y+80x+x-25y$$

Evaluate

$$-30z$$

Solution Steps

Combine 19y and 6y to get 25y.

$$-81x+25y-30z+80x+x-25y$$

Combine -81x and 80x to get -x.

$$-x+25y-30z+x-25y$$

Combine -x and x to get 0.

$$25y-30z-25y$$

Combine 25y and -25y to get 0.

$$-30z$$

Differentiate w.r.t. z

$$-30$$

Steps Using Definition of a Derivative

Combine 19y and 6y to get 25y.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-81x+25y-30z+80x+x-25y)$$

Combine -81x and 80x to get -x.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-x+25y-30z+x-25y)$$

Combine -x and x to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}z}(25y-30z-25y)$$

Combine 25y and -25y to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-30z)$$

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

$$-30z^{1-1}$$

Subtract 1 from 1.

$$-30z^{0}$$

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

$$-30$$