Solve 5b-2b+3b-b-3b+b

$$5 b - 2 b + 3 b - b - 3 b + b$$

Evaluate

$$3b$$

Solution Steps

Combine 5b and -2b to get 3b.

$$3b+3b-b-3b+b$$

Combine 3b and 3b to get 6b.

$$6b-b-3b+b$$

Combine 6b and -b to get 5b.

$$5b-3b+b$$

Combine 5b and -3b to get 2b.

$$2b+b$$

Combine 2b and b to get 3b.

$$3b$$

Differentiate w.r.t. b

$$3$$

Steps Using Definition of a Derivative

Combine 5b and -2b to get 3b.

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

Combine 3b and 3b to get 6b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(6b-b-3b+b)$$

Combine 6b and -b to get 5b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(5b-3b+b)$$

Combine 5b and -3b to get 2b.

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

Combine 2b and b to get 3b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(3b)$$

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

$$3b^{1-1}$$

Subtract 1 from 1.

$$3b^{0}$$

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

$$3\times 1$$

For any term t, t\times 1=t and 1t=t.

$$3$$