Solve 4a+2b-3a+b-a+b

$$4 a + 2 b - 3 a + b - a + b$$

Evaluate

$$4b$$

Solution Steps

Combine 4a and -3a to get a.

$$a+2b+b-a+b$$

Combine 2b and b to get 3b.

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

Combine a and -a to get 0.

$$3b+b$$

Combine 3b and b to get 4b.

$$4b$$

Differentiate w.r.t. b

$$4$$

Steps Using Definition of a Derivative

Combine 4a and -3a to get a.

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

Combine 2b and b to get 3b.

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

Combine a and -a to get 0.

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

Combine 3b and b to get 4b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(4b)$$

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

$$4b^{1-1}$$

Subtract 1 from 1.

$$4b^{0}$$

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

$$4\times 1$$

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

$$4$$