Pre-Calc: I need help with Deriving Exponential and logarithmic Functions (d/dx)?

Y^x = x^y x * ln(y) = y * ln(x) x * dy/y + ln(y) * dx = y * dx/x + ln(x) * dy (x/y) * dy - ln(x) * dy = (y/x) * dx - ln(y) * dx (x - y * ln(x)) * dy / y = (y - x * ln(y)) * dx / x dy/dx = y * (y - x * ln(y)) / (x * (x - y * ln(x))) dy/dx = (y^2 - xy * ln(y)) / (x^2 - xy * ln(x)).

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