Question

if x=log(xy) then dy by dx​

Answer 1

$\huge\underline\mathfrak\red{ANSWER}$

$x = log(x \times y) \\ \\ x = logx + logy \\ \\ x - logx = logy \\ \\ \frac{d(x - logx)}{dx} = \frac{d( logy)}{dx} \\ \\ 1 - \frac{1}{x} = \frac{1}{y} \frac{dy}{dx} \\ \\ \frac{(x - 1)y}{x} = \frac{dy}{dx}$

FORMULA USED

$differential \: of \: logx = \frac{1}{x} \\ differentiation \: of \: y = \frac{dy}{dx} \\ \\ log(a \times b) = loga + logb$

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