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

Question

TextLogarithmic Differentiation TechniqueDerivative of Functions in Parametric FormCBSE PYQ

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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

If x = e^(cos 3t) and y = e^(sin 3t), prove that dy/dx = – (y log x)/(x log y).

Show that : d/dx(|x|) = x/|x|, x ≠ 0

If y = cos³(sec² 2t), find dy/dt.

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