Solve 5a-8a+a-6a+3a

$$5 a - 8 a + a - 6 a + 3 a$$

Evaluate

$$-5a$$

Solution Steps

Combine 5a and -8a to get -3a.

$$-3a+a-6a+3a$$

Combine -3a and a to get -2a.

$$-2a-6a+3a$$

Combine -2a and -6a to get -8a.

$$-8a+3a$$

Combine -8a and 3a to get -5a.

$$-5a$$

Differentiate w.r.t. a

$$-5$$

Steps Using Definition of a Derivative

Combine 5a and -8a to get -3a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-3a+a-6a+3a)$$

Combine -3a and a to get -2a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-2a-6a+3a)$$

Combine -2a and -6a to get -8a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-8a+3a)$$

Combine -8a and 3a to get -5a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-5a)$$

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

$$-5a^{1-1}$$

Subtract 1 from 1.

$$-5a^{0}$$

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

$$-5$$