Solve (4v^2-7v+1)+(-3v^2+6v+5)

$$( 4 v ^ { 2 } - 7 v + 1 ) + ( - 3 v ^ { 2 } + 6 v + 5 )$$

Evaluate

$$v^{2}-v+6$$

Solution Steps

Combine 4v^{2} and -3v^{2} to get v^{2}.

$$v^{2}-7v+1+6v+5$$

Combine -7v and 6v to get -v.

$$v^{2}-v+1+5$$

Add 1 and 5 to get 6.

$$v^{2}-v+6$$

Differentiate w.r.t. v

$$2v-1$$

Steps Using Derivative Rule for Sum

Combine 4v^{2} and -3v^{2} to get v^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v^{2}-7v+1+6v+5)$$

Combine -7v and 6v to get -v.

$$\frac{\mathrm{d}}{\mathrm{d}v}(v^{2}-v+1+5)$$

Add 1 and 5 to get 6.

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

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.

$$2v-1$$