Solve -n+(-4)-(-4n)+6

$$- n + ( - 4 ) - ( - 4 n ) + 6$$

Evaluate

$$3n+2$$

Solution Steps

The opposite of -4n is 4n.

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

Add -4 and 6 to get 2.

$$-n+2+4n$$

Combine -n and 4n to get 3n.

$$3n+2$$

Differentiate w.r.t. n

$$3$$

Steps Using Derivative Rule for Sum

The opposite of -4n is 4n.

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

Add -4 and 6 to get 2.

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

Combine -n and 4n to get 3n.

$$\frac{\mathrm{d}}{\mathrm{d}n}(3n+2)$$

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}.

$$3n^{1-1}$$

Subtract 1 from 1.

$$3n^{0}$$

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

$$3\times 1$$

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

$$3$$