Solve 6v+2v+6v

$$6 v + 2 v + 6 v$$

Evaluate

$$14v$$

Solution Steps

Combine 6v and 2v to get 8v.

$$8v+6v$$

Combine 8v and 6v to get 14v.

$$14v$$

Differentiate w.r.t. v

$$14$$

Steps Using Definition of a Derivative

Combine 6v and 2v to get 8v.

$$\frac{\mathrm{d}}{\mathrm{d}v}(8v+6v)$$

Combine 8v and 6v to get 14v.

$$\frac{\mathrm{d}}{\mathrm{d}v}(14v)$$

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

$$14v^{1-1}$$

Subtract 1 from 1.

$$14v^{0}$$

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

$$14\times 1$$

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

$$14$$