If x^y = e^(x-y), prove that dy/dx = logx/(1+logx)²

Question

TextLogarithmic Differentiation TechniqueDerivative of Implicit Functions

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If √(1 – x²) + √(1 – y²) = a (x – y), prove that dy/dx = √(1 – y²)/√(1 – x²).

If y = (tan x)ˣ, then find dy/dx.

Derivative of Functions in Parametric Form

Find dy/dx, if (cos x)^y = (cos y)^x.

If yˣ = xʸ, then find dy/dx.

If y = x^(1/x), then find dy/dx at x = 1.

If xʸ = eˣ⁻ʸ, prove that dy/dx = log x / (1 + log x)².