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Class-12-science»Maths

if x ^y = e ^(x-y), then find dy/dx

$x^{y} = e^{(x - y)} A p p l y \ln, \ln x^{y} = \ln e^{(x - y)} y \ln x = x - y D i f f e r e n t i a t e, y (\frac{1}{x}) + \ln x * \frac{d y}{d x} = 1 - \frac{d y}{d x} \frac{d y}{d x} (\ln x + 1) = 1 - \frac{y}{x} = \frac{x - y}{x} \frac{d y}{d x} = \frac{x - y}{x (\ln x + 1)}$

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