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Differentiate w.r.t. D
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D\times \frac{\sqrt{8}}{\sqrt{125}}
Rewrite the square root of the division \sqrt{\frac{8}{125}} as the division of square roots \frac{\sqrt{8}}{\sqrt{125}}.
D\times \frac{2\sqrt{2}}{\sqrt{125}}
Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.
D\times \frac{2\sqrt{2}}{5\sqrt{5}}
Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.
D\times \frac{2\sqrt{2}\sqrt{5}}{5\left(\sqrt{5}\right)^{2}}
Rationalize the denominator of \frac{2\sqrt{2}}{5\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
D\times \frac{2\sqrt{2}\sqrt{5}}{5\times 5}
The square of \sqrt{5} is 5.
D\times \frac{2\sqrt{10}}{5\times 5}
To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.
D\times \frac{2\sqrt{10}}{25}
Multiply 5 and 5 to get 25.
\frac{D\times 2\sqrt{10}}{25}
Express D\times \frac{2\sqrt{10}}{25} as a single fraction.