d-d-x-W-x-W-x-is-lambert-W-function-

Question Number 95760 by M±th+et+s last updated on 27/May/20

\frac{d}{d (x)} (W (x)) = ?

W (x) i s l a m b e r t W f u n c t i o n

Answered by prakash jain last updated on 27/May/20

Do you mean W_{0} (x) by W (x) ?

y = {x e}^{x}

x = W (x) e^{W (x)}

\ln x = \ln W (x) + W (x)

\frac{1}{x} = \frac{1}{W (x)} \frac{d}{d x} W (x) + \frac{d}{d x} W (x)

\frac{1}{x} = \frac{1 + W (x)}{W (x)} \cdot \frac{d W (x)}{d (x)}

\frac{d}{d x} W (x) = \frac{W (x)}{x (1 + W (x))}

Commented by M±th+et+s last updated on 27/May/20

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