Evaluate
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Differentiate w.r.t. n
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n^{2}-\left(2\sqrt{2}\right)^{2}
Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
n^{2}-2^{2}\left(\sqrt{2}\right)^{2}
Expand \left(2\sqrt{2}\right)^{2}.
n^{2}-4\left(\sqrt{2}\right)^{2}
Calculate 2 to the power of 2 and get 4.
n^{2}-4\times 2
The square of \sqrt{2} is 2.
n^{2}-8
Multiply 4 and 2 to get 8.
\frac{\mathrm{d}}{\mathrm{d}n}(n^{2}-\left(2\sqrt{2}\right)^{2})
Consider \left(n-2\sqrt{2}\right)\left(n+2\sqrt{2}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{\mathrm{d}}{\mathrm{d}n}(n^{2}-2^{2}\left(\sqrt{2}\right)^{2})
Expand \left(2\sqrt{2}\right)^{2}.
\frac{\mathrm{d}}{\mathrm{d}n}(n^{2}-4\left(\sqrt{2}\right)^{2})
Calculate 2 to the power of 2 and get 4.
\frac{\mathrm{d}}{\mathrm{d}n}(n^{2}-4\times 2)
The square of \sqrt{2} is 2.
\frac{\mathrm{d}}{\mathrm{d}n}(n^{2}-8)
Multiply 4 and 2 to get 8.
2n^{2-1}
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}
Subtract 1 from 2.
2n
For any term t, t^{1}=t.