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If ​ x log y =log x then show that dy​/dx= y[1-logxlogy]/x(log 2 x)

If ​xlog y=log x then show that dy​/dx= y[1-logxlogy]/x(log2x)

Grade:11

1 Answers

Aditya Gupta
2081 Points
4 years ago
hey yamini
take log on both sides
log ​xlog y= log(log x)
logy*log x = log(log x)
differentiate both sides wrt x
(1/y)*(y’)*log x + logy*1/x= 1/xlog x
so, y’=  dy​/dx= y[1 – logxlogy]/x(log2x)
kindly approve :)

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