Solve 28a-(35a+23b)+45b-(21b-a)+6a=

$$28 a - ( 35 a + 23 b ) + 45 b - ( 21 b - a ) + 6 a =$$

Evaluate

$$b$$

Solution Steps

To find the opposite of 35a+23b, find the opposite of each term.

$$28a-35a-23b+45b-\left(21b-a\right)+6a$$

Combine 28a and -35a to get -7a.

$$-7a-23b+45b-\left(21b-a\right)+6a$$

Combine -23b and 45b to get 22b.

$$-7a+22b-\left(21b-a\right)+6a$$

To find the opposite of 21b-a, find the opposite of each term.

$$-7a+22b-21b-\left(-a\right)+6a$$

The opposite of -a is a.

$$-7a+22b-21b+a+6a$$

Combine 22b and -21b to get b.

$$-7a+b+a+6a$$

Combine -7a and a to get -6a.

$$-6a+b+6a$$

Combine -6a and 6a to get 0.

$$b$$

Differentiate w.r.t. b

$$1$$

Steps Using Definition of a Derivative

To find the opposite of 35a+23b, find the opposite of each term.

$$\frac{\mathrm{d}}{\mathrm{d}b}(28a-35a-23b+45b-\left(21b-a\right)+6a)$$

Combine 28a and -35a to get -7a.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-7a-23b+45b-\left(21b-a\right)+6a)$$

Combine -23b and 45b to get 22b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-7a+22b-\left(21b-a\right)+6a)$$

To find the opposite of 21b-a, find the opposite of each term.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-7a+22b-21b-\left(-a\right)+6a)$$

The opposite of -a is a.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-7a+22b-21b+a+6a)$$

Combine 22b and -21b to get b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-7a+b+a+6a)$$

Combine -7a and a to get -6a.

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

Combine -6a and 6a 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.

$$1$$