Solve -5ab+6ab+ab-ab+2ab-3ab+b=

$$- 5 a b + 6 a b + a b - a b + 2 a b - 3 a b + b =$$

Evaluate

$$b$$

Solution Steps

Combine -5ab and 6ab to get ab.

$$ab+ab-ab+2ab-3ab+b$$

Combine ab and ab to get 2ab.

$$2ab-ab+2ab-3ab+b$$

Combine 2ab and -ab to get ab.

$$ab+2ab-3ab+b$$

Combine ab and 2ab to get 3ab.

$$3ab-3ab+b$$

Combine 3ab and -3ab to get 0.

$$b$$

Differentiate w.r.t. b

$$1$$

Steps Using Definition of a Derivative

Combine -5ab and 6ab to get ab.

$$\frac{\mathrm{d}}{\mathrm{d}b}(ab+ab-ab+2ab-3ab+b)$$

Combine ab and ab to get 2ab.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2ab-ab+2ab-3ab+b)$$

Combine 2ab and -ab to get ab.

$$\frac{\mathrm{d}}{\mathrm{d}b}(ab+2ab-3ab+b)$$

Combine ab and 2ab to get 3ab.

$$\frac{\mathrm{d}}{\mathrm{d}b}(3ab-3ab+b)$$

Combine 3ab and -3ab 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.

$$1$$