Solve (r-7s+5)+(7r+6s)+(s+6)

$$( r - 7 s + 5 ) + ( 7 r + 6 s ) + ( s + 6 )$$

Evaluate

$$8r+11$$

Solution Steps

Combine r and 7r to get 8r.

$$8r-7s+5+6s+s+6$$

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

$$8r-s+5+s+6$$

Combine -s and s to get 0.

$$8r+5+6$$

Add 5 and 6 to get 11.

$$8r+11$$

Differentiate w.r.t. r

$$8$$

Steps Using Derivative Rule for Sum

Combine r and 7r to get 8r.

$$\frac{\mathrm{d}}{\mathrm{d}r}(8r-7s+5+6s+s+6)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(8r-s+5+s+6)$$

Combine -s and s to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}r}(8r+5+6)$$

Add 5 and 6 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}r}(8r+11)$$

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}.

$$8r^{1-1}$$

Subtract 1 from 1.

$$8r^{0}$$

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

$$8\times 1$$

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

$$8$$