Solve 2n-n^2-4n+3+n^2

$$2 n - n ^ { 2 } - 4 n + 3 + n ^ { 2 }$$

Evaluate

$$3-2n$$

Solution Steps

Combine 2n and -4n to get -2n.

$$-2n-n^{2}+3+n^{2}$$

Combine -n^{2} and n^{2} to get 0.

$$-2n+3$$

Differentiate w.r.t. n

$$-2$$

Steps Using Derivative Rule for Sum

Combine 2n and -4n to get -2n.

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

Combine -n^{2} and n^{2} to get 0.

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

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}.

$$-2n^{1-1}$$

Subtract 1 from 1.

$$-2n^{0}$$

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

$$-2$$