Find dy/dx of the functions. y^{x}=x^{y}

Question

Find dy/dx of the functions.
y^{x}=x^{y}

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Nevaeh 2 months 2021-10-05T03:47:24+00:00 1 Answer 0 views 0

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    2021-10-05T03:48:28+00:00

    Step-by-step explanation:

    y^(x) = x^(y)

    taking log on both the sides

    log y^(x) = log x^(y)

    x log y = y log x { log m^n = n log m }

    Now, differentiating both the sides with respect to x using chain rule.

    x/y dy/dx + log y = y. 1/x + log x dy/dx

    log y – y/x = log x dy/dx – x/y dy/dx

    (x log y – y) / y = {(y log x – x) / y } dy/dx

    dy/dx = {(x log y – y) / x } / {(y log x – x)/y}

    dy/dx = y (x log y – y) / x ( y log x – x)

    Hope this will helpful for you…!!!!!

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