Solve 5+8v+6v+6

$$5 + 8 v + 6 v + 6$$

Evaluate

$$14v+11$$

Solution Steps

Combine 8v and 6v to get 14v.

$$5+14v+6$$

Add 5 and 6 to get 11.

$$11+14v$$

Differentiate w.r.t. v

$$14$$

Steps Using Derivative Rule for Sum

Combine 8v and 6v to get 14v.

$$\frac{\mathrm{d}}{\mathrm{d}v}(5+14v+6)$$

Add 5 and 6 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}v}(11+14v)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. 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.

$$14$$