Solve (2n-2)+(2n-4)+n+2

$$( 2 n - 2 ) + ( 2 n - 4 ) + n + 2$$

Evaluate

$$5n-4$$

Solution Steps

Combine 2n and 2n to get 4n.

$$4n-2-4+n+2$$

Subtract 4 from -2 to get -6.

$$4n-6+n+2$$

Combine 4n and n to get 5n.

$$5n-6+2$$

Add -6 and 2 to get -4.

$$5n-4$$

Differentiate w.r.t. n

$$5$$

Steps Using Derivative Rule for Sum

Combine 2n and 2n to get 4n.

$$\frac{\mathrm{d}}{\mathrm{d}n}(4n-2-4+n+2)$$

Subtract 4 from -2 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}n}(4n-6+n+2)$$

Combine 4n and n to get 5n.

$$\frac{\mathrm{d}}{\mathrm{d}n}(5n-6+2)$$

Add -6 and 2 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}n}(5n-4)$$

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}.

$$5n^{1-1}$$

Subtract 1 from 1.

$$5n^{0}$$

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

$$5\times 1$$

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

$$5$$