Solve 2v_{3}-v_{3}+6v_{3}

$$2 v _ { 3 } - v _ { 3 } + 6 v _ { 3 }$$

Evaluate

$$7v_{3}$$

Solution Steps

Combine 2v_{3} and -v_{3} to get v_{3}.

$$v_{3}+6v_{3}$$

Combine v_{3} and 6v_{3} to get 7v_{3}.

$$7v_{3}$$

Differentiate w.r.t. v_3

$$7$$

Steps Using Definition of a Derivative

Combine 2v_{3} and -v_{3} to get v_{3}.

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

Combine v_{3} and 6v_{3} to get 7v_{3}.

$$\frac{\mathrm{d}}{\mathrm{d}v_{3}}(7v_{3})$$

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

$$7v_{3}^{1-1}$$

Subtract 1 from 1.

$$7v_{3}^{0}$$

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

$$7\times 1$$

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

$$7$$