Solve +{(-2a+b)-(-a+b-c)+a}

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

Evaluate

$$c$$

Solution Steps

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

$$-2a+b-\left(-a\right)-b-\left(-c\right)+a$$

The opposite of -c is c.

$$-2a+b-\left(-a\right)-b+c+a$$

Combine b and -b to get 0.

$$-2a-\left(-a\right)+c+a$$

Combine -2a and a to get -a.

$$-a-\left(-a\right)+c$$

Multiply -1 and -1 to get 1.

$$-a+a+c$$

Combine -a and a to get 0.

$$c$$

Differentiate w.r.t. c

$$1$$

Steps Using Definition of a Derivative

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

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

The opposite of -c is c.

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

Combine b and -b to get 0.

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

Combine -2a and a to get -a.

$$\frac{\mathrm{d}}{\mathrm{d}c}(-a-\left(-a\right)+c)$$

Multiply -1 and -1 to get 1.

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

Combine -a and a to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c)$$

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

$$c^{1-1}$$

Subtract 1 from 1.

$$c^{0}$$

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

$$1$$