Solve -a+b+2b-2c+3a+2c-3b=

$$- a + b + 2 b - 2 c + 3 a + 2 c - 3 b =$$

Evaluate

$$2a$$

Solution Steps

Combine b and 2b to get 3b.

$$-a+3b-2c+3a+2c-3b$$

Combine -2c and 2c to get 0.

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

Combine 3b and -3b to get 0.

$$-a+3a$$

Combine -a and 3a to get 2a.

$$2a$$

Differentiate w.r.t. a

$$2$$

Steps Using Definition of a Derivative

Combine b and 2b to get 3b.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-a+3b-2c+3a+2c-3b)$$

Combine -2c and 2c to get 0.

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

Combine 3b and -3b to get 0.

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

Combine -a and 3a to get 2a.

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

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

$$2a^{1-1}$$

Subtract 1 from 1.

$$2a^{0}$$

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

$$2\times 1$$

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

$$2$$