If (sin x)ʸ = yᶜᵒˢ ˣ, then find dy/dx.

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TextDerivative of a FunctionLogarithmic Differentiation Technique

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The derivative of sin (x²) w.r.t. x, at x = √π is :

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.

If f(x) = |tan 2x|, then find the value of f′(x) at x = π/3.

If x = e^(x/y), prove that dy/dx = (log x – 1)/(log x)²

Check the differentiability of f(x) = {x² + 1, 0 ≤ x < 1; 3 – x, 1 ≤ x ≤ 2} at x = 1.