Solve 8v+7v-2v

$$8 v + 7 v - 2 v$$

Evaluate

$$13v$$

Solution Steps

Combine 8v and 7v to get 15v.

$$15v-2v$$

Combine 15v and -2v to get 13v.

$$13v$$

Differentiate w.r.t. v

$$13$$

Steps Using Definition of a Derivative

Combine 8v and 7v to get 15v.

$$\frac{\mathrm{d}}{\mathrm{d}v}(15v-2v)$$

Combine 15v and -2v to get 13v.

$$\frac{\mathrm{d}}{\mathrm{d}v}(13v)$$

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

$$13v^{1-1}$$

Subtract 1 from 1.

$$13v^{0}$$

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

$$13\times 1$$

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

$$13$$