Solve n+1quadn+2quadn+n

$$n + 1 \quad n + 2 \quad n + n$$

Evaluate

$$5n$$

Solution Steps

Combine n and 1n to get 2n.

$$2n+2n+n$$

Combine 2n and 2n to get 4n.

$$4n+n$$

Combine 4n and n to get 5n.

$$5n$$

Differentiate w.r.t. n

$$5$$

Steps Using Definition of a Derivative

Combine n and 1n to get 2n.

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

Combine 2n and 2n to get 4n.

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

Combine 4n and n to get 5n.

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

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.

$$5$$