Solve a-b-c-b-c+2c-a

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

Evaluate

$$-2b$$

Solution Steps

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

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

Combine -c and -c to get -2c.

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

Combine -2c and 2c to get 0.

$$a-2b-a$$

Combine a and -a to get 0.

$$-2b$$

Differentiate w.r.t. b

$$-2$$

Steps Using Definition of a Derivative

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

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

Combine -c and -c to get -2c.

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

Combine -2c and 2c to get 0.

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

Combine a and -a to get 0.

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

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

$$-2b^{1-1}$$

Subtract 1 from 1.

$$-2b^{0}$$

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

$$-2$$