Solve 2r+5+2r+r+4r-3

$$2 r + 5 + 2 r + r + 4 r - 3$$

Evaluate

$$9r+2$$

Solution Steps

Combine 2r and 2r to get 4r.

$$4r+5+r+4r-3$$

Combine 4r and r to get 5r.

$$5r+5+4r-3$$

Combine 5r and 4r to get 9r.

$$9r+5-3$$

Subtract 3 from 5 to get 2.

$$9r+2$$

Differentiate w.r.t. r

$$9$$

Steps Using Derivative Rule for Sum

Combine 2r and 2r to get 4r.

$$\frac{\mathrm{d}}{\mathrm{d}r}(4r+5+r+4r-3)$$

Combine 4r and r to get 5r.

$$\frac{\mathrm{d}}{\mathrm{d}r}(5r+5+4r-3)$$

Combine 5r and 4r to get 9r.

$$\frac{\mathrm{d}}{\mathrm{d}r}(9r+5-3)$$

Subtract 3 from 5 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}r}(9r+2)$$

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}.

$$9r^{1-1}$$

Subtract 1 from 1.

$$9r^{0}$$

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

$$9\times 1$$

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

$$9$$