Solve b-8+3b-4-5b+12

$$b-8+3b-4-5b+12$$

Evaluate

$$-b$$

Solution Steps

Combine b and 3b to get 4b.

$$4b-8-4-5b+12$$

Subtract 4 from -8 to get -12.

$$4b-12-5b+12$$

Combine 4b and -5b to get -b.

$$-b-12+12$$

Add -12 and 12 to get 0.

$$-b$$

Differentiate w.r.t. b

$$-1$$

Steps Using Definition of a Derivative

Combine b and 3b to get 4b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(4b-8-4-5b+12)$$

Subtract 4 from -8 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}b}(4b-12-5b+12)$$

Combine 4b and -5b to get -b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-b-12+12)$$

Add -12 and 12 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-b)$$

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

$$-b^{1-1}$$

Subtract 1 from 1.

$$-b^{0}$$

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

$$-1$$