Solve +2n+2n+2n+8n+0n+0n

$$+ 2 n + 2 n + 2 n + 8 n + 0 n + 0 n$$

Evaluate

$$14n$$

Solution Steps

Combine 2n and 2n to get 4n.

$$4n+2n+8n+0n+0n$$

Combine 4n and 2n to get 6n.

$$6n+8n+0n+0n$$

Combine 6n and 8n to get 14n.

$$14n+0n+0n$$

Anything times zero gives zero.

$$14n+0+0n$$

Anything times zero gives zero.

$$14n+0+0$$

Add 0 and 0 to get 0.

$$14n$$

Differentiate w.r.t. n

$$14$$

Steps Using Definition of a Derivative

Combine 2n and 2n to get 4n.

$$\frac{\mathrm{d}}{\mathrm{d}n}(4n+2n+8n+0n+0n)$$

Combine 4n and 2n to get 6n.

$$\frac{\mathrm{d}}{\mathrm{d}n}(6n+8n+0n+0n)$$

Combine 6n and 8n to get 14n.

$$\frac{\mathrm{d}}{\mathrm{d}n}(14n+0n+0n)$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}n}(14n+0+0n)$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}n}(14n+0+0)$$

Add 0 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}n}(14n)$$

The derivative of ax^{n} is nax^{n-1}.

$$14n^{1-1}$$

Subtract 1 from 1.

$$14n^{0}$$

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

$$14\times 1$$

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

$$14$$