Solve {l}{1^2+2^2+}{+n^2}

$$\left. \begin{array} { l } { 1 ^ { 2 } + 2 ^ { 2 } + } \\ { + n ^ { 2 } } \end{array} \right.$$

Evaluate

$$n^{2}+5$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$1+2^{2}+n^{2}$$

Calculate 2 to the power of 2 and get 4.

$$1+4+n^{2}$$

Add 1 and 4 to get 5.

$$5+n^{2}$$

Differentiate w.r.t. n

$$2n$$

Steps Using Derivative Rule for Sum

Calculate 1 to the power of 2 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}n}(1+2^{2}+n^{2})$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}n}(1+4+n^{2})$$

Add 1 and 4 to get 5.

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

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}.

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

Subtract 1 from 2.

$$2n^{1}$$

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

$$2n$$