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

$$\frac{d}{d\left(x\right)}\left(W\left(x\right)\right)=?$$$$W\left(x\right)islambertWfunction$$

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

$$\mathrm{Do}\mathrm{you}\mathrm{mean}{W}_0\left(x\right)\mathrm{by}W\left(x\right)?$$$$y={xe}^x$$$$x=W\left(x\right)e^{W\left(x\right)}$$$$\ln x=\ln W\left(x\right)+W\left(x\right)$$$$\frac{1}{x}=\frac{1}{W\left(x\right)}\frac{d}{dx}W\left(x\right)+\frac{d}{dx}W\left(x\right)$$$$\frac{1}{x}=\frac{1+W\left(x\right)}{W\left(x\right)}\cdot \frac{dW\left(x\right)}{d\left(x\right)}$$$$\frac{d}{dx}W\left(x\right)=\frac{W\left(x\right)}{x(1+W\left(x\right))}$$

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

$$yessir.thankyou$$

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