Solve (3v^2-6v+1)+(-2v^2+7v+4)

$$( 3 v ^ { 2 } - 6 v + 1 ) + ( - 2 v ^ { 2 } + 7 v + 4 )$$

Evaluate

$$v^{2}+v+5$$

Solution Steps

Combine 3v^{2} and -2v^{2} to get v^{2}.

$$v^{2}-6v+1+7v+4$$

Combine -6v and 7v to get v.

$$v^{2}+v+1+4$$

Add 1 and 4 to get 5.

$$v^{2}+v+5$$

Differentiate w.r.t. v

$$2v+1$$

Steps Using Derivative Rule for Sum

Combine 3v^{2} and -2v^{2} to get v^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v^{2}-6v+1+7v+4)$$

Combine -6v and 7v to get v.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v^{2}+v+1+4)$$

Add 1 and 4 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v^{2}+v+5)$$

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}.

$$2v^{2-1}+v^{1-1}$$

Subtract 1 from 2.

$$2v^{1}+v^{1-1}$$

Subtract 1 from 1.

$$2v^{1}+v^{0}$$

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

$$2v+v^{0}$$

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

$$2v+1$$