Evaluate
-40\sqrt{5}n
Differentiate w.r.t. n
-40\sqrt{5}
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\left(-\sqrt{6400+40^{2}}\right)n
Calculate 80 to the power of 2 and get 6400.
\left(-\sqrt{6400+1600}\right)n
Calculate 40 to the power of 2 and get 1600.
\left(-\sqrt{8000}\right)n
Add 6400 and 1600 to get 8000.
\left(-40\sqrt{5}\right)n
Factor 8000=40^{2}\times 5. Rewrite the square root of the product \sqrt{40^{2}\times 5} as the product of square roots \sqrt{40^{2}}\sqrt{5}. Take the square root of 40^{2}.
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